M6444 Stochastic models of Markov type
Faculty of ScienceSpring 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:
- 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
- Epidemiology and modeling (programme PřF, N-MBB)
- 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.
M6444 Stochastic models of Markov type
Faculty of ScienceSpring 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
- Epidemiology and modeling (programme PřF, N-MBB)
- 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.
M6444 Stochastic models of Markov type
Faculty of ScienceSpring 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:
- 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
- Epidemiology and modeling (programme PřF, N-MBB)
- 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.
M6444 Stochastic models of Markov type
Faculty of ScienceSpring 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:
- 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
- Epidemiology and modeling (programme PřF, N-MBB)
- 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.
M6444 Stochastic models of Markov type
Faculty of ScienceSpring 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:
- 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
- Epidemiology and modeling (programme PřF, N-MBB)
- 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.
M6444 Stochastic models of Markov type
Faculty of ScienceSpring 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:
- 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
- Epidemiology and modeling (programme PřF, N-MBB)
- 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.
M6444 Stochastic models of Markov type
Faculty of ScienceSpring 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:
- 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.
M6444 Stochastic models of Markov type
Faculty of Sciencespring 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:
- 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.
M6444 Stochastic models of Markov type
Faculty of ScienceSpring 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:
M6444/02: 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.
M6444 Stochastic models
Faculty of ScienceSpring 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:
- 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.
M6444 Stochastic models
Faculty of ScienceSpring 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:
- 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.
M6444 Stochastic models
Faculty of ScienceSpring 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:
M6444/02: 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.
M6444 Stochastic models
Faculty of ScienceSpring 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:
M6444/02: 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.
M6444 Stochastic models
Faculty of ScienceSpring 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:
- 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
- Applied Mathematics - Geography (programme PřF, B-GR)
- Mathematics (programme PřF, B-MA)
- 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.
M6444 Stochastic models II
Faculty of ScienceSpring 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:
M6444/02: 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
- Applied Mathematics - Geography (programme PřF, B-GR)
- Mathematics (programme PřF, B-MA)
- 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.
M6444 Stochastic models II
Faculty of ScienceSpring 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:
- 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
- Applied Mathematics - Geography (programme PřF, B-GR)
- Mathematics (programme PřF, B-MA)
- 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.
M6444 Stochastic models II
Faculty of ScienceSpring 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:
- 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
- Applied Mathematics - Geography (programme PřF, B-GR)
- Mathematics (programme PřF, B-MA)
- 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.
M6444 Stochastic models II
Faculty of ScienceSpring 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:
- 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
- Applied Mathematics - Geography (programme PřF, B-GR)
- Mathematics (programme PřF, B-MA)
- 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.
M6444 Stochastic models II
Faculty of ScienceSpring 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:
- 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
- Applied Mathematics - Geography (programme PřF, B-GR)
- Mathematics (programme PřF, B-MA)
- 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.
M6444 Stochastic models II
Faculty of ScienceSpring 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:
- 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
- Applied Mathematics - Geography (programme PřF, B-GR)
- Mathematics (programme PřF, B-MA)
- 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.
M6444 Stochastic models II
Faculty of ScienceSpring 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:
- 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
- Applied Mathematics - Geography (programme PřF, B-GR)
- Mathematics - Economics (programme PřF, N-AM)
- Mathematics (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, N-AM)
- 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.
M6444 Stochastic models II
Faculty of ScienceSpring 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
- Applied Mathematics - Geography (programme PřF, B-GR)
- Mathematics (programme PřF, B-MA)
- Language of instruction
- Czech
- Further Comments
- The course is taught annually.
M6444 Stochastic models of Markov type
Faculty of ScienceAutumn 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.
M6444 Stochastic models of Markov type
Faculty of ScienceAutumn 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.
M6444 Stochastic models of Markov type
Faculty of ScienceAutumn 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.
M6444 Stochastic models of Markov type
Faculty of Scienceautumn 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.
M6444 Stochastic models of Markov type
Faculty of ScienceAutumn 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.
M6444 Stochastic models of Markov type
Faculty of ScienceAutumn 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.
M6444 Stochastic models
Faculty of Sciencespring 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
- Applied Mathematics - Geography (programme PřF, B-GR)
- Mathematics (programme PřF, B-MA)
- 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.
M6444 Stochastic models II
Faculty of ScienceSpring 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
- Applied Mathematics - Geography (programme PřF, B-GR)
- Mathematics (programme PřF, B-MA)
- 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.
M6444 Stochastic models II
Faculty of ScienceSpring 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
- Applied Mathematics - Geography (programme PřF, B-GR)
- Mathematics (programme PřF, B-MA)
- 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.
- Enrolment Statistics (recent)