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### Markov chains

 Code: 36921 ECTS: 5.0 Lecturers in charge: doc. dr. sc. Rudi Mrazović doc. dr. sc. Hrvoje Planinić Lecturers: dr. sc. Ivan Biočić - Exercises dr. sc. Ivana Valentić - Exercises English level: 1,0,0 All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.

### 1. komponenta

Lecture typeTotal
Lectures 30
Exercises 30
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
Prerequisit for:
Enrollment :
Passed : Integral calculus of functions of several variables
Passed : Probability
 5. semester Not active Izborni predmet 1, 2 - Regular study - Mathematics 6. semester Izborni predmet 1, 2 - Regular study - 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

# Predavanja za grupu prof. Basraka

Kako je najavljeno, predavanje za ponedjeljak 8.11. na teme Jako Markovljevo svojstvo te Definicija povratnosti i prolaznosti neće se održati u učionici, no može se pogledati na https://youtu.be/UxsZAnvINpw