PřF:M5444 Markov chains - Course Information
M5444 Markov chains
Faculty of ScienceAutumn 2024
- Extent and Intensity
- 2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
- Teacher(s)
- RNDr. Marie Budíková, Dr. (lecturer)
- Guaranteed by
- RNDr. Marie Budíková, Dr.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Thu 9:00–10:50 M3,01023
- Timetable of Seminar Groups:
- Prerequisites
- M3121 Probability and Statistics I || M4122 Probability and Statistics II
M3121 and M4122 - 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
- Mathematical and Statistical Methods in Economics (programme ESF, N-KME)
- Course objectives
- The aim of the course is:
to explain to students the important concepts of Markov chains theory with discrete time and continuous time;
to show students the application of Markov chains in practice;
teach students how to solve problems on Markov chains using MATLAB. - Learning outcomes
- After completing this course, students will be able to:
- model simple real-life situations using homogeneous Markov chains with discrete or continuous time and discrete state space;
- estimate the model parameters from real data;
- to use Markov chains in practical applications (for example bonus-malus system, applications in genetics, a description of the operation of the production line);
- to solve the problems associated with the Markov chains using MATLAB system. - Syllabus
- Introduction to study of stochastic processes, functional characteristics of stochastic process.
- Markov chains with discrete time: the transition probabilities, classification of states, irreducible and reducible chains, stationary distribution, transient states, estimates of the probability of transition, Markov chains with estimation of transitions, Markov chains with disconted estimation of transitions
- Finite Markov chains with continuous time: basic references, Chapman-Kolmogorov's equality, Kolmogorov's differential equations and their solving, limited division of states.
- Countable Markov chains with continuous 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.
- 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 with "open book". It consists of three or four examples. The examination is scored 100 points. To successfully pass the exam, 51 points will suffice.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
Information on completion of the course: Ukončení zápočtem je možné pouze pro studenty, kteří nestudují studijní program Matematika.
The course is taught annually. - Teacher's information
- To successfully complete the course, it is necessary to be familiar with the basic concepts of the theory of homogeneous Markov chains with discrete and continuous time and to be able to apply the acquired knowledge in solving simple real situations using the MATLAB system.
- Enrolment Statistics (recent)
- Permalink: https://is.muni.cz/course/sci/autumn2024/M5444