Markov chains

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Detailed data
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Consultations schedule

Code:	36921
ECTS:	5.0
Lecturers in charge:	doc. dr. sc. Rudi Mrazović doc. dr. sc. Hrvoje Planinić
Lecturers:	Ela Đimoti , mag. math. - Exercises Daniela Ivanković , mag. math. - 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 : Integral calculus of functions of several variables
Passed : Probability

5. semester

Izborni predmet 1, 2 - Regular study - Mathematics

6. semester Not active

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

2021-11-07

Author: Hrvoje Planinić

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Markov chains

1. komponenta

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Predavanja za grupu prof. Basraka

FACULTY OF SCIENCE