Markov chains

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Markov chains

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Consultations schedule

Code:	36921
ECTS:	5.0
Lecturers in charge:	prof. dr. sc. Bojan Basrak - Lectures prof. dr. sc. Zoran Vondraček - Lectures
Lecturers:	Ivan Biočić - Exercises Hrvoje Planinić - 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.

Load:

1. komponenta

Lecture type Total

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:

Prerequisit for:

Enrollment :
Passed : Probability

5. semester

Izborni predmet 1, 2 - Mandatory studij - Mathematics

6. semester Not active

Izborni predmet 1, 2 - Mandatory studij - Mathematics

Consultations schedule:

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Markov chains

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FACULTY OF SCIENCE