M5444 Markov chains

Faculty of Science
Autumn 2022
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
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
Wed 10:00–11:50 M2,01021
  • Timetable of Seminar Groups:
M5444/01: Wed 12:00–12:50 MP1,01014, Wed 12:00–12:50 M2,01021, M. Budíková
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
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.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2022, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2022/M5444