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Markov Processes - NMTP562

Title:	Markovské procesy
Guaranteed by:	Department of Probability and Mathematical Statistics (32-KPMS)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2021
Semester:	summer
E-Credits:	6
Hours per week, examination:	summer s.:4/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Additional information:	http://simu0292.utia.cas.cz/seidler/teaching.html

Guarantor:	RNDr. Jan Seidler, CSc.
Class:	M Mgr. PMSE M Mgr. PMSE > Volitelné
Classification:	Mathematics > Probability and Statistics
Pre-requisite :	NMTP432
Is interchangeable with:	NSTP176

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Annotation -

Last update: T_KPMS (16.05.2013)

The very basic results of the continuous time Markov processes theory will be treated.

Aim of the course -

Last update: T_KPMS (16.05.2013)

The subject is aimed at the study of basic properties of continuous time

Markov processes taking values in general state spaces and the emphasis is

put on Feller processes and large-time behaviour.

Course completion requirements -

Last update: RNDr. Jitka Zichová, Dr. (13.05.2023)

Oral exam.

Literature - Czech

Last update: T_KPMS (16.05.2013)

L.C.G. Rogers, D. Williams: Diffusion Markov processes and martingales. Vol. 1., Cambridge univ. press, 1994.

S.N. Ethier, T.G. Kurtz: Markov processes, Wiley, 1986.

Teaching methods -

Last update: T_KPMS (16.05.2013)

Lecture.

Requirements to the exam -

Last update: RNDr. Jitka Zichová, Dr. (13.05.2023)

Oral exam according to sylabus.

Syllabus -

Last update: T_KPMS (16.05.2013)

1. The Markov property, transition functions and operators associated with them, construction

of a process with a given transition function, shift operators and homogenous prpocesses.

2. Feller processes in locally compact spaces, their C0 semigroups, resolvents and generators,

the Hille-Yosida theorem, properties of sample paths, strong Markov processes.

3. Jump processes, processes with independent increments, Lévy processes, the Lévy-

Khinchin formula.

4. Diffusion processes: local characteristics, construction via stochastic differential equations,

the Kolmogorov equation.

5. Elementary ergodic theory: invariant measures, transient and recurrent processes, basic

results on existence of an invariant measure, (Krylov-Bogolyubov, Sunyach), strong Feller

processes, uniqueness and stability of invariant measures.

Entry requirements -

Last update: RNDr. Jan Seidler, CSc. (28.05.2019)

Students should have mastered the basics of probability theory and have some idea about Markov chains. A knowledge of stochastic analysis, or even stochastic differential equations, is desirable but not absolutely necessary – contact the lecturer.