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Lecturer(s)
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Fačevicová Kamila, Mgr. Ph.D.
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Hron Karel, prof. RNDr. Ph.D.
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Course content
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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.
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Learning activities and teaching methods
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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
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Learning outcomes
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Understand basics of Markov chains (processes) theory and their applications.
Application Apply probability theory to stochastical modelling of processes.
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Prerequisites
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Basic knowledge of probability theory.
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Assessment methods and criteria
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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).
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Recommended literature
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Hron, K., & Kunderová, P. (2012). Markovovy řetězce a jejich aplikace. Olomouc: Univerzita Palackého v Olomouci.
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J. Kalas. (1993). Markovove ret'azce. MF UK Bratislava.
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J. NORRIS. (1998). Markov chains. Cambridge University Press.
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L. Maixner. (1991). Markovovy procesy a jejich aplikace. UP Olomouc.
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L. Piatka. (1981). Markovove procesy. Alfa Bratislava (skripta VŠD Žilina).
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R.P. Dobrow. (2016). Introduction to stochastic processes with R.. Wiley, Chichester.
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Z. Prášková, P. Lachout. (1998). Základy náhodných procesů. Nakladatelství UK Praha.
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