Course: Markov Chains

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Course title Markov Chains
Course code KMA/MR
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
Semester Summer
Number of ECTS credits 3
Language of instruction Czech, English
Status of course Compulsory, Compulsory-optional, Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
Lecturer(s)
  • Hron Karel, doc. RNDr. Ph.D.
Course content
1. Motivation, Markov chains with discrete time - basic terms. 2. Transition probabilities, classification of states of a chain. 3. Classification of states of a chain. 4. Decomposition of a state set. 5. Markov chains with continuous time, Kolmogorov differential equations. 6. Stationary distribution, Poisson process. 7. Further known processes. 8. Markov chains with yields. 9. Simulations of Markov chains. 10. Applications of Markov chains in queueing theory. 11. Further applications of Markov chains.

Learning activities and teaching methods
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming), Demonstration
  • Attendace - 39 hours per semester
  • Preparation for the Course Credit - 15 hours per semester
  • Preparation for the Exam - 35 hours per semester
Learning outcomes
Understand basics of Markov chains (processes) theory and their applications.
Application Apply probability theory to stochastical modelling of processes.
Prerequisites
Basic knowledge of probability theory.

Assessment methods and criteria
Written exam

Credit: the student has to pass one written test (theory + examples), i.e. to obtain at least two thirds of the possible points in the test).
Recommended literature
  • Hron, K., & Kunderová, P. (2012). Markovovy řetězce a jejich aplikace. Olomouc: Univerzita Palackého v Olomouci.
  • J. Kalas. (1993). Markovove ret'azce. MF UK Bratislava.
  • J. NORRIS. (1998). Markov chains. Cambridge University Press.
  • L. Maixner. (1991). Markovovy procesy a jejich aplikace. UP Olomouc.
  • L. Piatka. (1981). Markovove procesy. Alfa Bratislava (skripta VŠD Žilina).
  • Z. Prášková, P. Lachout. (1998). Základy náhodných procesů. Nakladatelství UK Praha.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Applied Mathematics (2014) Mathematics courses 1 Summer
Faculty of Science Applications of Mathematics in Economy (2015) Mathematics courses 1 Summer