M6444 Stochastic models of Markov type

Faculty of Science
Spring 2024
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
doc. PaedDr. RNDr. Stanislav Katina, Ph.D. (assistant)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 19. 2. to Sun 26. 5. Thu 8:00–9:50 M5,01013
  • Timetable of Seminar Groups:
M6444/01: Mon 19. 2. to Sun 26. 5. Fri 12:00–13:50 MP1,01014, Fri 12:00–13:50 M3,01023, M. Budíková
Prerequisites
M3121 Probability and Statistics I || M4122 Probability and Statistics II
M5444
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of the course is to acquaint students:
with the using of simulations in the analysis of stochastic models;
with the properties of some selected probability distributions;
with important models of queuing systems;
with the properties of the Galton-Watson branching process.
Learning outcomes
After completing this course, the students will be able to
use statistical toolbox of MATLAB to generate pseudo-random numbers from different probability distributions;
check the conformity of the empirical distribution with the theoretical distribution;
calculate the important characteristics of queuing systems;
analyze the behavior of Galton - Watson branching process.
Syllabus
  • The issue of modeling, using simulations, random number generators.
  • An important probability distribution, their properties, methods of verification.
  • Basic concepts of queuing theory, queuing systems with unlimited and limited capacity, optimization problems in queuing systems.
  • The probability generating function and its application in the analysis of Galton - Watson branching process.
Literature
  • SKALSKÁ, Hana. Stochastické modelování. Vyd. 2., rozšíř. a uprav. Hradec Králové: Gaudeamus, 2006, 162 s. ISBN 807041488X. info
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Teaching methods
The weekly class schedule consists of 2 hour lecture and 2 hour of class exercises with MATLAB system.
Assessment methods
The final exam is written, with "open book" and consists of three or four examples. Examples are evaluated on a scale from 0 to 100. It is necessary to obtain at least 51%.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents.

The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics.

Assessment in all cases may be in Czech and English, at the student's choice.

The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2025.

M6444 Stochastic models of Markov type

Faculty of Science
Spring 2025
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
doc. PaedDr. RNDr. Stanislav Katina, Ph.D. (assistant)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M3121 Probability and Statistics I || M4122 Probability and Statistics II
M5444
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of the course is to acquaint students:
with the using of simulations in the analysis of stochastic models;
with the properties of some selected probability distributions;
with important models of queuing systems;
with the properties of the Galton-Watson branching process.
Learning outcomes
After completing this course, the students will be able to
use statistical toolbox of MATLAB to generate pseudo-random numbers from different probability distributions;
check the conformity of the empirical distribution with the theoretical distribution;
calculate the important characteristics of queuing systems;
analyze the behavior of Galton - Watson branching process.
Syllabus
  • The issue of modeling, using simulations, random number generators.
  • An important probability distribution, their properties, methods of verification.
  • Basic concepts of queuing theory, queuing systems with unlimited and limited capacity, optimization problems in queuing systems.
  • The probability generating function and its application in the analysis of Galton - Watson branching process.
Literature
  • SKALSKÁ, Hana. Stochastické modelování. Vyd. 2., rozšíř. a uprav. Hradec Králové: Gaudeamus, 2006, 162 s. ISBN 807041488X. info
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Teaching methods
The weekly class schedule consists of 2 hour lecture and 2 hour of class exercises with MATLAB system.
Assessment methods
The final exam is written, with "open book" and consists of three or four examples. Examples are evaluated on a scale from 0 to 100. It is necessary to obtain at least 51%.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents.

The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics.

Assessment in all cases may be in Czech and English, at the student's choice.

The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024.

M6444 Stochastic models of Markov type

Faculty of Science
Spring 2023
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
doc. PaedDr. RNDr. Stanislav Katina, Ph.D. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 10:00–11:50 M6,01011
  • Timetable of Seminar Groups:
M6444/01: Mon 12:00–12:50 M3,01023, Mon 13:00–13:50 MP1,01014, M. Budíková
Prerequisites
M3121 Probability and Statistics I || M4122 Probability and Statistics II
M5444
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of the course is to acquaint students:
with the using of simulations in the analysis of stochastic models;
with the properties of some selected probability distributions;
with important models of queuing systems;
with the properties of the Galton-Watson branching process.
Learning outcomes
After completing this course, the students will be able to
use statistical toolbox of MATLAB to generate pseudo-random numbers from different probability distributions;
check the conformity of the empirical distribution with the theoretical distribution;
calculate the important characteristics of queuing systems;
analyze the behavior of Galton - Watson branching process.
Syllabus
  • The issue of modeling, using simulations, random number generators.
  • An important probability distribution, their properties, methods of verification.
  • Basic concepts of queuing theory, queuing systems with unlimited and limited capacity, optimization problems in queuing systems.
  • The probability generating function and its application in the analysis of Galton - Watson branching process.
Literature
  • SKALSKÁ, Hana. Stochastické modelování. Vyd. 2., rozšíř. a uprav. Hradec Králové: Gaudeamus, 2006, 162 s. ISBN 807041488X. info
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Teaching methods
The weekly class schedule consists of 2 hour lecture and 2 hour of class exercises with MATLAB system.
Assessment methods
The final exam is written, with "open book" and consists of three or four examples. Examples are evaluated on a scale from 0 to 100. It is necessary to obtain at least 51%.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents.

The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics.

Assessment in all cases may be in Czech and English, at the student's choice.

The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2024, Spring 2025.

M6444 Stochastic models of Markov type

Faculty of Science
Spring 2022
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
doc. PaedDr. RNDr. Stanislav Katina, Ph.D. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 8:00–9:50 M6,01011
  • Timetable of Seminar Groups:
M6444/01: Fri 10:00–10:50 M6,01011, Fri 11:00–11:50 MP2,01014a, M. Budíková
Prerequisites
M3121 Probability and Statistics I || M4122 Probability and Statistics II
M5444
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of the course is to acquaint students:
with the using of simulations in the analysis of stochastic models;
with the properties of some selected probability distributions;
with important models of queuing systems;
with the properties of the Galton-Watson branching process.
Learning outcomes
After completing this course, the students will be able to
use statistical toolbox of MATLAB to generate pseudo-random numbers from different probability distributions;
check the conformity of the empirical distribution with the theoretical distribution;
calculate the important characteristics of queuing systems;
analyze the behavior of Galton - Watson branching process.
Syllabus
  • The issue of modeling, using simulations, random number generators.
  • An important probability distribution, their properties, methods of verification.
  • Basic concepts of queuing theory, queuing systems with unlimited and limited capacity, optimization problems in queuing systems.
  • The probability generating function and its application in the analysis of Galton - Watson branching process.
Literature
  • SKALSKÁ, Hana. Stochastické modelování. Vyd. 2., rozšíř. a uprav. Hradec Králové: Gaudeamus, 2006, 162 s. ISBN 807041488X. info
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Teaching methods
The weekly class schedule consists of 2 hour lecture and 2 hour of class exercises with MATLAB system.
Assessment methods
The final exam is written, with "open book" and consists of three or four examples. Examples are evaluated on a scale from 0 to 100. It is necessary to obtain at least 51%.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents.

The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics.

Assessment in all cases may be in Czech and English, at the student's choice.

The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models of Markov type

Faculty of Science
Spring 2021
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 1. 3. to Fri 14. 5. Wed 8:00–9:50 online_M3
  • Timetable of Seminar Groups:
M6444/01: Mon 1. 3. to Fri 14. 5. Mon 14:00–15:50 online_MP1, M. Budíková
Prerequisites
M3121 Probability and Statistics I || M4122 Probability and Statistics II
M5444
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of the course is to acquaint students:
with the using of simulations in the analysis of stochastic models;
with the properties of some selected probability distributions;
with important models of queuing systems;
with the properties of the Galton-Watson branching process.
Learning outcomes
After completing this course, the students will be able to
use statistical toolbox of MATLAB to generate pseudo-random numbers from different probability distributions;
check the conformity of the empirical distribution with the theoretical distribution;
calculate the important characteristics of queuing systems;
analyze the behavior of Galton - Watson branching process.
Syllabus
  • The issue of modeling, using simulations, random number generators.
  • An important probability distribution, their properties, methods of verification.
  • Basic concepts of queuing theory, queuing systems with unlimited and limited capacity, optimization problems in queuing systems.
  • The probability generating function and its application in the analysis of Galton - Watson branching process.
Literature
  • SKALSKÁ, Hana. Stochastické modelování. Vyd. 2., rozšíř. a uprav. Hradec Králové: Gaudeamus, 2006, 162 s. ISBN 807041488X. info
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Teaching methods
The weekly class schedule consists of 2 hour lecture and 2 hour of class exercises with MATLAB system.
Assessment methods
The final exam is written, with "open book" and consists of three or four examples. Examples are evaluated on a scale from 0 to 100. It is necessary to obtain at least 51%.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents.

The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics.

Assessment in all cases may be in Czech and English, at the student's choice.

The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models of Markov type

Faculty of Science
Spring 2020
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 12:00–13:50 M5,01013
  • Timetable of Seminar Groups:
M6444/01: Fri 8:00–9:50 M4,01024, Fri 8:00–9:50 MP1,01014, M. Budíková
Prerequisites
M3121 Probability and Statistics I || M4122 Probability and Statistics II
M5444
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of the course is to acquaint students:
with the using of simulations in the analysis of stochastic models;
with the properties of some selected probability distributions;
with important models of queuing systems;
with the properties of the Galton-Watson branching process.
Learning outcomes
After completing this course, the students will be able to
use statistical toolbox of MATLAB to generate pseudo-random numbers from different probability distributions;
check the conformity of the empirical distribution with the theoretical distribution;
calculate the important characteristics of queuing systems;
analyze the behavior of Galton - Watson branching process.
Syllabus
  • The issue of modeling, using simulations, random number generators.
  • An important probability distribution, their properties, methods of verification.
  • Basic concepts of queuing theory, queuing systems with unlimited and limited capacity, optimization problems in queuing systems.
  • The probability generating function and its application in the analysis of Galton - Watson branching process.
Literature
  • SKALSKÁ, Hana. Stochastické modelování. Vyd. 2., rozšíř. a uprav. Hradec Králové: Gaudeamus, 2006, 162 s. ISBN 807041488X. info
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Teaching methods
The weekly class schedule consists of 2 hour lecture and 1 hour of class exercises with MATLAB system.
Assessment methods
The final exam is written, with "open book" and consists of three or four examples. Examples are evaluated on a scale from 0 to 100. It is necessary to obtain at least 51%.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents.

The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics.

Assessment in all cases may be in Czech and English, at the student's choice.

The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models of Markov type

Faculty of Science
Spring 2019
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 18. 2. to Fri 17. 5. Mon 14:00–15:50 M2,01021
  • Timetable of Seminar Groups:
M6444/01: Mon 18. 2. to Fri 17. 5. Mon 16:00–16:50 M6,01011, Mon 16:00–16:50 MP1,01014, M. Budíková
Prerequisites
M3121 Probability and Statistics I || M4122 Probability and Statistics II
M5444
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
After completing this course, the students will be able to - use statistical toolbox of MATLAB to generate pseudo-random numbers from different probability distributions; - check the conformity of the empirical distribution with the theoretical distribution; - calculate the important characteristics of queuing systems; - analyze the behavior of Galton - Watson process.
Learning outcomes
After completing this course, the students will be able to
use statistical toolbox of MATLAB to generate pseudo-random numbers from different probability distributions;
check the conformity of the empirical distribution with the theoretical distribution;
calculate the important characteristics of queuing systems;
analyze the behavior of Galton - Watson branching process.
Syllabus
  • The issue of modeling, using simulations, random number generators.
  • An important probability distribution, their properties, methods of verification.
  • Basic concepts of queuing theory, queuing systems with unlimited and limited capacity, optimization problems in queuing systems.
  • The probability generating function and its application in the analysis of Galton - Watson branching process.
Literature
  • SKALSKÁ, Hana. Stochastické modelování. Vyd. 2., rozšíř. a uprav. Hradec Králové: Gaudeamus, 2006, 162 s. ISBN 807041488X. info
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Teaching methods
The weekly class schedule consists of 2 hour lecture and 1 hour of class exercises with MATLAB system.
Assessment methods
The final exam is written, with "open book" and consists of three or four examples. Examples are evaluated on a scale from 0 to 100. It is necessary to obtain at least 51%.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models of Markov type

Faculty of Science
spring 2018
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 8:00–9:50 M5,01013
  • Timetable of Seminar Groups:
M6444/01: Tue 12:00–12:50 M1,01017, Tue 12:00–12:50 MP1,01014, M. Budíková
Prerequisites
M3121 Probability and Statistics I || M4122 Probability and Statistics II
M5444
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
After completing this course, the students will be able to - use statistical toolbox of MATLAB to generate pseudo-random numbers from different probability distributions; - check the conformity of the empirical distribution with the theoretical distribution; - calculate the important characteristics of queuing systems; - analyze the behavior of Galton - Watson process.
Learning outcomes
After completing this course, the students will be able to
use statistical toolbox of MATLAB to generate pseudo-random numbers from different probability distributions;
check the conformity of the empirical distribution with the theoretical distribution;
calculate the important characteristics of queuing systems;
analyze the behavior of Galton - Watson branching process.
Syllabus
  • The issue of modeling, using simulations, random number generators.
  • An important probability distribution, their properties, methods of verification.
  • Basic concepts of queuing theory, queuing systems with unlimited and limited capacity, optimization problems in queuing systems.
  • The probability generating function and its application in the analysis of Galton - Watson branching process.
Literature
  • SKALSKÁ, Hana. Stochastické modelování. Vyd. 2., rozšíř. a uprav. Hradec Králové: Gaudeamus, 2006, 162 s. ISBN 807041488X. info
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Teaching methods
The weekly class schedule consists of 2 hour lecture and 1 hour of class exercises with MATLAB system.
Assessment methods
The final exam is written, with "open book" and consists of three or four examples. Examples are evaluated on a scale from 0 to 100. It is necessary to obtain at least 51%.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models of Markov type

Faculty of Science
Spring 2017
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 20. 2. to Mon 22. 5. Mon 8:00–9:50 M1,01017
  • Timetable of Seminar Groups:
M6444/01: Mon 20. 2. to Mon 22. 5. Tue 9:00–9:50 MP1,01014, Tue 9:00–9:50 M3,01023, M. Budíková
M6444/02: Mon 20. 2. to Mon 22. 5. Tue 10:00–10:50 MP1,01014, Tue 10:00–10:50 M3,01023, M. Budíková
Prerequisites
M3121 Probability and Statistics I || M4122 Probability and Statistics II
M5444
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
After completing this course, the students will be able to - use statistical toolbox of MATLAB to generate pseudo-random numbers from different probability distributions; - check the conformity of the empirical distribution with the theoretical distribution; - calculate the important characteristics of queuing systems; - analyze the behavior of Galton - Watson process.
Syllabus
  • The issue of modeling, using simulations, random number generators.
  • An important probability distribution, their properties, methods of verification.
  • Basic concepts of queuing theory, queuing systems with unlimited and limited capacity, optimization problems in queuing systems.
  • The probability generating function and its application in the analysis of Galton - Watson branching process.
Literature
  • SKALSKÁ, Hana. Stochastické modelování. Vyd. 2., rozšíř. a uprav. Hradec Králové: Gaudeamus, 2006, 162 s. ISBN 807041488X. info
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Teaching methods
The weekly class schedule consists of 2 hour lecture and 1 hour of class exercises with MATLAB system.
Assessment methods
The final exam is written, with "open book" and consists of three or four examples. Examples are evaluated on a scale from 0 to 100. It is necessary to obtain at least 51%.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models

Faculty of Science
Spring 2016
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 10:00–11:50 M2,01021
  • Timetable of Seminar Groups:
M6444/01: Fri 8:00–8:50 MP1,01014, Fri 8:00–8:50 MP2,01014a, Fri 8:00–8:50 M2,01021, M. Budíková
Prerequisites
M3121 Probability and Statistics I || M4122 Probability and Statistics II
M5444
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
After completing this course, the students will be able to - use statistical toolbox of MATLAB to generate pseudo-random numbers from different probability distributions; - check the conformity of the empirical distribution with the theoretical distribution; - calculate the important characteristics of queuing systems; - analyze the behavior of Galton - Watson process.
Syllabus
  • The issue of modeling, using simulations, random number generators.
  • An important probability distribution, their properties, methods of verification.
  • Basic concepts of queuing theory, queuing systems with unlimited and limited capacity, optimization problems in queuing systems.
  • The probability generating function and its application in the analysis of Galton - Watson branching process.
Literature
  • SKALSKÁ, Hana. Stochastické modelování. Vyd. 2., rozšíř. a uprav. Hradec Králové: Gaudeamus, 2006, 162 s. ISBN 807041488X. info
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Teaching methods
The weekly class schedule consists of 2 hour lecture and 1 hour of class exercises with MATLAB system.
Assessment methods
The final exam is written, with "open book" and consists of three or four examples. Examples are evaluated on a scale from 0 to 100. It is necessary to obtain at least 51%.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models

Faculty of Science
Spring 2015
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 8:00–9:50 M5,01013
  • Timetable of Seminar Groups:
M6444/01: Wed 13:00–13:50 M6,01011, Wed 13:00–13:50 MP1,01014
Prerequisites
M3121 Probability and Statistics I || M4122 Probability and Statistics II
M5444
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
After completing this course, the students will be able to - use statistical toolbox of MATLAB to generate pseudo-random numbers from different probability distributions; - check the conformity of the empirical distribution with the theoretical distribution; - calculate the important characteristics of queuing systems; - analyze the behavior of Galton - Watson process.
Syllabus
  • The issue of modeling, using simulations, random number generators.
  • An important probability distribution, their properties, methods of verification.
  • Basic concepts of queuing theory, queuing systems with unlimited and limited capacity, optimization problems in queuing systems.
  • The probability generating function and its application in the analysis of Galton - Watson branching process.
Literature
  • SKALSKÁ, Hana. Stochastické modelování. Vyd. 2., rozšíř. a uprav. Hradec Králové: Gaudeamus, 2006, 162 s. ISBN 807041488X. info
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Teaching methods
The weekly class schedule consists of 2 hour lecture and 1 hour of class exercises with MATLAB system.
Assessment methods
The final exam is written, with "open book" and consists of three or four examples. Examples are evaluated on a scale from 0 to 100. It is necessary to obtain at least 51%.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models

Faculty of Science
Spring 2014
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 14:00–15:50 M1,01017
  • Timetable of Seminar Groups:
M6444/01: Mon 14:00–14:50 MP1,01014, Mon 14:00–14:50 M6,01011, M. Budíková
M6444/02: Mon 15:00–15:50 MP1,01014, Mon 15:00–15:50 M6,01011, M. Budíková
Prerequisites
M3121 Probability and Statistics I || M4122 Probability and Statistics II
M5444
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
This course deals with the possibilities of some simple modeling of real situations in which random effects operate. Attention is paid to analytical and simulation tools for the probabilistic description of dynamical systems with discrete states and their use in the analysis of queuing systems. After completing this course the students will be able to model simple real situations using analytical and simulation methods. They also will be able to use MATLAB system.
Syllabus
  • The issue of modeling, using simulations, random number generators.
  • An important probability distribution, their properties, methods of verification.
  • Controlled homogeneous Markov chain, Howard iterative procedure.
  • Basic concepts of queuing theory, queuing systems with unlimited and limited capacity, optimization problems in queuing systems.
Literature
  • SKALSKÁ, Hana. Stochastické modelování. Vyd. 2., rozšíř. a uprav. Hradec Králové: Gaudeamus, 2006, 162 s. ISBN 807041488X. info
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Teaching methods
The weekly class schedule consists of 2 hour lecture and 1 hour of class exercises with MATLAB system.
Assessment methods
The final exam is written, consists of four examples. Examples are evaluated on a scale from 0 to 100. It is necessary to obtain at least 51%.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models

Faculty of Science
Spring 2013
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 8:00–9:50 M1,01017
  • Timetable of Seminar Groups:
M6444/01: Mon 9:00–9:50 MP1,01014, Mon 9:00–9:50 M6,01011, M. Budíková
M6444/02: Mon 8:00–8:50 MP1,01014, Mon 8:00–8:50 M6,01011, M. Budíková
Prerequisites
M3121 Probability and Statistics I || M4122 Probability and Statistics II
M5444
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
This course deals with the possibilities of some simple modeling of real situations in which random effects operate. Attention is paid to analytical and simulation tools for the probabilistic description of dynamical systems with discrete states and their use in the analysis of queuing systems. After completing this course the students will be able to model simple real situations using analytical and simulation methods. They also will be able to use MATLAB system.
Syllabus
  • The issue of modeling, using simulations, random number generators.
  • An important probability distribution, their properties, methods of verification.
  • Controlled homogeneous Markov chain, Howard iterative procedure.
  • Basic concepts of queuing theory, queuing systems with unlimited and limited capacity, optimization problems in queuing systems.
Literature
  • SKALSKÁ, Hana. Stochastické modelování. Vyd. 2., rozšíř. a uprav. Hradec Králové: Gaudeamus, 2006, 162 s. ISBN 807041488X. info
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Teaching methods
The weekly class schedule consists of 2 hour lecture and 1 hour of class exercises with MATLAB system.
Assessment methods
The final exam is written, consists of four examples. Examples are evaluated on a scale from 0 to 100. It is necessary to obtain at least 51%.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models

Faculty of Science
Spring 2012
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 8:00–9:50 M3,01023
  • Timetable of Seminar Groups:
M6444/01: Fri 10:00–10:50 M3,01023, Fri 10:00–10:50 MP1,01014
Prerequisites
M3121 Probability and Statistics I || M4122 Probability and Statistics II
M5444
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
This course deals with the possibilities of some simple modeling of real situations in which random effects operate. Attention is paid to analytical and simulation tools for the probabilistic description of dynamical systems with discrete states and their use in the analysis of queuing systems. After completing this course the students will be able to model simple real situations using analytical and simulation methods. They also will be able to use MATLAB system.
Syllabus
  • The issue of modeling, using simulations, random number generators.
  • An important probability distribution, their properties, methods of verification.
  • Controlled homogeneous Markov chain, Howard iterative procedure.
  • Basic concepts of queuing theory, queuing systems with unlimited and limited capacity, optimization problems in queuing systems.
Literature
  • SKALSKÁ, Hana. Stochastické modelování. Vyd. 2., rozšíř. a uprav. Hradec Králové: Gaudeamus, 2006, 162 s. ISBN 807041488X. info
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Teaching methods
The weekly class schedule consists of 2 hour lecture and 1 hour of class exercises with MATLAB system.
Assessment methods
The examination is written.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models II

Faculty of Science
Spring 2011
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 8:00–9:50 M2,01021
  • Timetable of Seminar Groups:
M6444/01: Mon 8:00–8:50 M4,01024, Mon 8:00–8:50 MP1,01014, M. Budíková
M6444/02: Mon 9:00–9:50 M4,01024, Mon 9:00–9:50 MP1,01014, M. Budíková
Prerequisites
M3121 Probability and Statistics I || M4122 Probability and Statistics II
M5444
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
This subject is about special case of stochastic processes - processes with continuos time, which has Markov property. Reflected are as finite, as countable Markov chains. Attention is paid also to queuing systems. Upon completing this course, students will be able to simulate simple real-world situations using homogeneous Markov’s chains with continuous time. They also will be able to use MATLAB system.
Syllabus
  • Finite Markov chains with continuos time: basic references, Chapman-Kolmogorov's equality, Kolmogorov's differential equations and their solving, limited division of states. Countable Markov chains with continuos time: solution of Kolmogorov's equations for countable chains, limited division of states for countable chains, Poisson's process, Yule's process, general process of birth, linear process of birth and death, general process of birth and death. Stochastic models in queuing theory: queuing systems and their classification, queuing systems with Poisson arrivals and exponential service times.
Literature
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • PRÁŠKOVÁ, Zuzana and Petr LACHOUT. Základy náhodných procesů. 1. vyd. Praha: Karolinum, 1998, 146 s. ISBN 8071846880. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Teaching methods
The weekly class schedule consists of 2 hour lecture and 1 hour of class exercises with MATLAB system.
Assessment methods
The examination is written.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models II

Faculty of Science
Spring 2010
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 13:00–14:50 M3,01023
  • Timetable of Seminar Groups:
M6444/01: Mon 8:00–8:50 MP1,01014, Mon 8:00–8:50 M3,01023
Prerequisites
M3121 Probability and Statistics I || M4122 Probability and Statistics II
M5444
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
This subject is about special case of stochastic processes - processes with continuos time, which has Markov property. Reflected are as finite, as countable Markov chains. Attention is paid also to queuing systems. Upon completing this course, students will be able to simulate simple real-world situations using homogeneous Markov’s chains with continuous time. They also will be able to use MATLAB system.
Syllabus
  • Finite Markov chains with continuos time: basic references, Chapman-Kolmogorov's equality, Kolmogorov's differential equations and their solving, limited division of states. Countable Markov chains with continuos time: solution of Kolmogorov's equations for countable chains, limited division of states for countable chains, Poisson's process, Yule's process, general process of birth, linear process of birth and death, general process of birth and death. Stochastic models in queuing theory: queuing systems and their classification, queuing systems with Poisson arrivals and exponential service times.
Literature
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • PRÁŠKOVÁ, Zuzana and Petr LACHOUT. Základy náhodných procesů. 1. vyd. Praha: Karolinum, 1998, 146 s. ISBN 8071846880. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Teaching methods
The weekly class schedule consists of 2 hour lecture and 1 hour of class exercises with MATLAB system.
Assessment methods
The examination is written.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models II

Faculty of Science
Spring 2009
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 8:00–9:50 M3,01023
  • Timetable of Seminar Groups:
M6444/01: Thu 10:00–10:50 MP1,01014, Thu 10:00–10:50 M3,01023
Prerequisites
M3121 Probability and Statistics I || M4122 Probability and Statistics II
M5444
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
This subject is about special case of stochastic processes - processes with continuos time, which has Markov property. Reflected are as finite, as countable Markov chains. Attention is paid also to queuing systems. Upon completing this course, students will be able to simulate simple real-world situations using homogeneous Markov’s chains with continuous time. They also will be able to use MATLAB system.
Syllabus
  • Finite Markov chains with continuos time: basic references, Chapman-Kolmogorov's equality, Kolmogorov's differential equations and their solving, limited division of states. Countable Markov chains with continuos time: solution of Kolmogorov's equations for countable chains, limited division of states for countable chains, Poisson's process, Yule's process, general process of birth, linear process of birth and death, general process of birth and death. Stochastic models in queuing theory: queuing systems and their classification, queuing systems with Poisson arrivals and exponential service times.
Literature
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • PRÁŠKOVÁ, Zuzana and Petr LACHOUT. Základy náhodných procesů. 1. vyd. Praha: Karolinum, 1998, 146 s. ISBN 8071846880. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Assessment methods
The weekly class schedule consists of 2 hour lecture and 1 hour of class exercises with MATLAB system. The examination is written.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models II

Faculty of Science
Spring 2008
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
prof. RNDr. Jana Jurečková, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 14:00–15:50 UP2
  • Timetable of Seminar Groups:
M6444/01: Tue 11:00–11:50 M3,04005 - dříve Janáčkovo nám. 2a, Tue 11:00–11:50 N41
Prerequisites
M3121 Probability and Statistics I || M4122 Probability and Statistics II
M5444
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
This subject is about special case of stochastic processes - processes with continuos time, which has Markov property. Reflected are as finite, as countable Markov chains. Attention is paid also to queuing systems.
Syllabus
  • Finite Markov chains with continuos time: basic references, Chapman-Kolmogorov's equality, Kolmogorov's differential equations and their solving, limited division of states. Countable Markov chains with continuos time: solution of Kolmogorov's equations for countable chains, limited division of states for countable chains, Poisson's process, Yule's process, general process of birth, linear process of birth and death, general process of birth and death. Stochastic models in queuing theory: queuing systems and their classification, queuing systems with Poisson arrivals and exponential service times.
Literature
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • PRÁŠKOVÁ, Zuzana and Petr LACHOUT. Základy náhodných procesů. 1. vyd. Praha: Karolinum, 1998, 146 s. ISBN 8071846880. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Assessment methods (in Czech)
Výuka se koná každý týden v rozsahu 2h přednáška, 1h cvičení. Zkouška je písemná.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models II

Faculty of Science
Spring 2007
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
prof. RNDr. Jana Jurečková, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: RNDr. Marie Budíková, Dr.
Timetable
Thu 10:00–11:50 UP2
  • Timetable of Seminar Groups:
M6444/01: Tue 10:00–10:50 M3,04005 - dříve Janáčkovo nám. 2a, Tue 10:00–10:50 N21
Prerequisites
M3121 Probability and Statistics I || M4122 Statistics
M5444
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
This subject is about special case of stochastic processes - processes with continuos time, which has Markov property. Reflected are as finite, as countable Markov chains. Attention is paid also to queuing systems.
Syllabus
  • Finite Markov chains with continuos time: basic references, Chapman-Kolmogorov's equality, Kolmogorov's differential equations and their solving, limited division of states. Countable Markov chains with continuos time: solution of Kolmogorov's equations for countable chains, limited division of states for countable chains, Poisson's process, Yule's process, general process of birth, linear process of birth and death, general process of birth and death. Stochastic models in queuing theory: queuing systems and their classification, queuing systems with Poisson arrivals and exponential service times.
Literature
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • PRÁŠKOVÁ, Zuzana and Petr LACHOUT. Základy náhodných procesů. 1. vyd. Praha: Karolinum, 1998, 146 s. ISBN 8071846880. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Assessment methods (in Czech)
Výuka se koná každý týden v rozsahu 2h přednáška, 1h cvičení. Zkouška je písemná.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models II

Faculty of Science
Spring 2006
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
prof. RNDr. Jana Jurečková, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: RNDr. Marie Budíková, Dr.
Timetable
Thu 12:00–13:50 N41
  • Timetable of Seminar Groups:
M6444/01: Thu 14:00–14:50 M3,04005 - dříve Janáčkovo nám. 2a, Thu 14:00–14:50 N41
Prerequisites
M3121 Probability || M4122 Statistics
M5444
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
This subject is about special case of stochastic processes - processes with continuos time, which has Markov property. Reflected are as finite, as countable Markov chains. Attention is paid also to queuing systems.
Syllabus
  • Finite Markov chains with continuos time: basic references, Chapman-Kolmogorov's equality, Kolmogorov's differential equations and their solving, limited division of states. Countable Markov chains with continuos time: solution of Kolmogorov's equations for countable chains, limited division of states for countable chains, Poisson's process, Yule's process, general process of birth, linear process of birth and death, general process of birth and death. Stochastic models in queuing theory: queuing systems and their classification, queuing systems with Poisson arrivals and exponential service times.
Literature
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • PRÁŠKOVÁ, Zuzana and Petr LACHOUT. Základy náhodných procesů. 1. vyd. Praha: Karolinum, 1998, 146 s. ISBN 8071846880. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Assessment methods (in Czech)
Výuka se koná každý týden v rozsahu 2h přednáška, 1h cvičení. Zkouška je písemná.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models II

Faculty of Science
Spring 2005
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
prof. RNDr. Jana Jurečková, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: RNDr. Marie Budíková, Dr.
Timetable
Thu 14:00–15:50 N41
  • Timetable of Seminar Groups:
M6444/01: Fri 10:00–10:50 M3,04005 - dříve Janáčkovo nám. 2a, Fri 10:00–10:50 N41, M. Budíková
Prerequisites
M3121 Probability || M4122 Statistics
M5444
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
This subject is about special case of stochastic processes - processes with continuos time, which has Markov property. Reflected are as finite, as countable Markov chains. Attention is paid also to queuing systems.
Syllabus
  • Finite Markov chains with continuos time: basic references, Chapman-Kolmogorov's equality, Kolmogorov's differential equations and their solving, limited division of states. Countable Markov chains with continuos time: solution of Kolmogorov's equations for countable chains, limited division of states for countable chains, Poisson's process, Yule's process, general process of birth, linear process of birth and death, general process of birth and death. Stochastic models in queuing theory: queuing systems and their classification, queuing systems with Poisson arrivals and exponential service times.
Literature
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • PRÁŠKOVÁ, Zuzana and Petr LACHOUT. Základy náhodných procesů. 1. vyd. Praha: Karolinum, 1998, 146 s. ISBN 8071846880. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Assessment methods (in Czech)
Výuka se koná každý týden v rozsahu 2h přednáška, 1h cvičení. Zkouška je písemná.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models II

Faculty of Science
Spring 2004
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
prof. RNDr. Jana Jurečková, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: RNDr. Marie Budíková, Dr.
Timetable of Seminar Groups
M6444/01: No timetable has been entered into IS. M. Budíková
Prerequisites (in Czech)
M3121 Probability || M4122 Statistics
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models of Markov type

Faculty of Science
Autumn 2024

The course is not taught in Autumn 2024

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites (in Czech)
M3121 Probability and Statistics I || M4122 Probability and Statistics II
Course Enrolment Limitations
The course is offered to students of any study field.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models of Markov type

Faculty of Science
Autumn 2023

The course is not taught in Autumn 2023

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites (in Czech)
M3121 Probability and Statistics I || M4122 Probability and Statistics II
Course Enrolment Limitations
The course is offered to students of any study field.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models of Markov type

Faculty of Science
Autumn 2022

The course is not taught in Autumn 2022

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites (in Czech)
M3121 Probability and Statistics I || M4122 Probability and Statistics II
Course Enrolment Limitations
The course is offered to students of any study field.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models of Markov type

Faculty of Science
autumn 2021

The course is not taught in autumn 2021

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites (in Czech)
M3121 Probability and Statistics I || M4122 Probability and Statistics II
Course Enrolment Limitations
The course is offered to students of any study field.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models of Markov type

Faculty of Science
Autumn 2020

The course is not taught in Autumn 2020

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites (in Czech)
M3121 Probability and Statistics I || M4122 Probability and Statistics II
Course Enrolment Limitations
The course is offered to students of any study field.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models of Markov type

Faculty of Science
Autumn 2019

The course is not taught in Autumn 2019

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites (in Czech)
M3121 Probability and Statistics I || M4122 Probability and Statistics II
Course Enrolment Limitations
The course is offered to students of any study field.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models

Faculty of Science
spring 2012 - acreditation

The information about the term spring 2012 - acreditation is not made public

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M3121 Probability and Statistics I || M4122 Probability and Statistics II
M5444
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
This course deals with the possibilities of some simple modeling of real situations in which random effects operate. Attention is paid to analytical and simulation tools for the probabilistic description of dynamical systems with discrete states and their use in the analysis of queuing systems. After completing this course the students will be able to model simple real situations using analytical and simulation methods. They also will be able to use MATLAB system.
Syllabus
  • The issue of modeling, using simulations, random number generators.
  • An important probability distribution, their properties, methods of verification.
  • Controlled homogeneous Markov chain, Howard iterative procedure.
  • Basic concepts of queuing theory, queuing systems with unlimited and limited capacity, optimization problems in queuing systems.
Literature
  • SKALSKÁ, Hana. Stochastické modelování. Vyd. 2., rozšíř. a uprav. Hradec Králové: Gaudeamus, 2006, 162 s. ISBN 807041488X. info
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Teaching methods
The weekly class schedule consists of 2 hour lecture and 1 hour of class exercises with MATLAB system.
Assessment methods
The examination is written.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models II

Faculty of Science
Spring 2011 - only for the accreditation
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M3121 Probability || M4122 Probability and Statistics II
M5444
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
This subject is about special case of stochastic processes - processes with continuos time, which has Markov property. Reflected are as finite, as countable Markov chains. Attention is paid also to queuing systems. Upon completing this course, students will be able to simulate simple real-world situations using homogeneous Markov’s chains with continuous time. They also will be able to use MATLAB system.
Syllabus
  • Finite Markov chains with continuos time: basic references, Chapman-Kolmogorov's equality, Kolmogorov's differential equations and their solving, limited division of states. Countable Markov chains with continuos time: solution of Kolmogorov's equations for countable chains, limited division of states for countable chains, Poisson's process, Yule's process, general process of birth, linear process of birth and death, general process of birth and death. Stochastic models in queuing theory: queuing systems and their classification, queuing systems with Poisson arrivals and exponential service times.
Literature
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • PRÁŠKOVÁ, Zuzana and Petr LACHOUT. Základy náhodných procesů. 1. vyd. Praha: Karolinum, 1998, 146 s. ISBN 8071846880. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Teaching methods
The weekly class schedule consists of 2 hour lecture and 1 hour of class exercises with MATLAB system.
Assessment methods
The examination is written.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M6444 Stochastic models II

Faculty of Science
Spring 2008 - for the purpose of the accreditation
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
prof. RNDr. Jana Jurečková, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: RNDr. Marie Budíková, Dr.
Prerequisites
M3121 Probability || M4122 Statistics
M5444
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
This subject is about special case of stochastic processes - processes with continuos time, which has Markov property. Reflected are as finite, as countable Markov chains. Attention is paid also to queuing systems.
Syllabus
  • Finite Markov chains with continuos time: basic references, Chapman-Kolmogorov's equality, Kolmogorov's differential equations and their solving, limited division of states. Countable Markov chains with continuos time: solution of Kolmogorov's equations for countable chains, limited division of states for countable chains, Poisson's process, Yule's process, general process of birth, linear process of birth and death, general process of birth and death. Stochastic models in queuing theory: queuing systems and their classification, queuing systems with Poisson arrivals and exponential service times.
Literature
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • PRÁŠKOVÁ, Zuzana and Petr LACHOUT. Základy náhodných procesů. 1. vyd. Praha: Karolinum, 1998, 146 s. ISBN 8071846880. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Assessment methods (in Czech)
Výuka se koná každý týden v rozsahu 2h přednáška, 1h cvičení. Zkouška je písemná.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (recent)