1. komponenta

Lecture type	Total
Lectures	30
Exercises	30

COURSE AIMS AND OBJECTIVES: The goal of the course is to learn fundamental results of the theory of homogeneous Markov chains with discrete time, and apply these results in mathematical modelling of random phenomena.

COURSE DESCRIPTION AND SYLLABUS:
1. Introduction to Markov chains.
2. Definition and basic properties. Transition matrix. Classes.
3. Hitting times. Probability absorptions.
4. Strong Markov property.
5. Recurrency and transiency. Analysis of random walks.
6. Invariant and stationary distribution. Limiting distribution.
7. Convergence towards equilibrium.
8. Ergodic theorem.
9. Time reversal.
10. Introduction to Markov chains in continuous time.
11. Application of Markov chains. Electric networks.
12. Application of Markov chains in biology.
13. Decision Markov processes.
14. MCMC (Markov chain Monte Carlo).

1. Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues, P. Bremaud, Springer Verlag, 1999.
2. Markov Chains, J. R. Norris, Cambridge University Press, 1997.
3. Adventures in Stochastic Processes, S. I. Resnick, Birkhäuser, 1992.

Izborni predmet 1, 2 - Regular study - Theoretical Mathematics

Izborni predmet 1, 2 - Regular study - Theoretical Mathematics