Course for international guest/part time students
- Faculty
- Faculty of Science
- Organization
- TTK Department of Probability Theory and Statistics
- Code
- difoml1u0um17em
- Title
- Markov chains in discrete and continuous time (l)
- Usual semester
- Autumn
- Published semester
- 2026/27/1
- ECTS
- 3
- Language
- en
- Learning outcomes
- Knowledge: getting familiar with the modern notions and methods of Markov chains
- Course content
- Stochastic processes: Markov property, strong Markov property, homogeneity. Markov chains with discrete parameters: definition, transition matrix, classification of states. Period, recurrence. Convergence of transition probabilities. Stationary distribution. Central limit theorem for irreducible, positive recurrent Markov chain. Transition probabilities with taboo states. Regular measure, Doeblin's quotient theorem. Inverted Markov chain. Absorption probabilities. Perron-Frobenius theorems. Markov chains with continuous parameters: definition, transition matrix, derivative at zero, infinitesimal generator. Examples: Poisson process, birth and death processes.
- Assessment method
- oral exam
- Bibliography
- lecture notes
- Recommended bibliography
- K. L. Chung: Markov Processes with Stationary Transition Probabilities. J. R. Norris: Markov Chains.