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### Markov chains

 Code: 160517 ECTS: 5.0 Lecturers in charge: doc. dr. sc. Rudi Mrazović - Lectures doc. dr. sc. Hrvoje Planinić - Lectures Lecturers: Ivan Biočić, mag. math. - Exercises dr. sc. Ivana Valentić - Exercises

### 1. komponenta

Lecture typeTotal
Lectures 30
Exercises 30
* Load is given in academic hour (1 academic hour = 45 minutes)
Description:
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).
Literature:
1. P. Bremaud: Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues
2. J. R. Norris: Markov Chains
3. S. I. Resnick: Adventures in Stochastic Processes
 1. semester Izborni predmet 1, 2 - Regular study - Theoretical Mathematics 2. semester Izborni predmet 1, 2 - Regular study - Theoretical Mathematics
Consultations schedule:

### Content

Link to the course web page: https://web.math.pmf.unizg.hr/nastava/mala/

Link to the notices web page: https://www.pmf.unizg.hr/math/predmet/marlan_a

# Vježbe za grupu asistenta Planinića

Idući tjedan, u četvrtak 11.11., vježbe će se održati u skraćenom i malo ranijem terminu: od 10:05 (točno) do 11:15. Nadalje, umjesto u četvrtak 18.11. (državni praznik), vježbe će se održati u utorak 16.11. od 8:15-10 u prostoriji A102

Lijep pozdrav,

Hrvoje Planinić