MAGIC093: Introduction to Markov processes, with coupling and convergence rates, and applications

Course details

A core MAGIC course

Semester

Spring 2019
Monday, January 21st to Friday, March 29th

Hours

Live lecture hours
20
Recorded lecture hours
0
Total advised study hours
80

Timetable

Sundays
00:05 - 00:55
Sundays
00:05 - 00:55

Description

Markov processes in discrete and continuous time will be presented for elementary and general state spaces and for some jump & so called linear-Markov (semi-Markov) processes in continuous times. Standard stuff will include generators, Dynkin’s formula, ergodicity for finite state spaces, strong Markov, Feller & strong Feller properties. A bit more advanced material will include coupling & recurrence applied to convergence rates and to queueing & reliability systems.

Prerequisites

Some basic knowledge about Markov chains is highly desirable.

Syllabus

1. Stochastic processes. Definitions of a Markov process. 2. Examples: Random Walks. Generators. Chapman-Kolmogorov equations. 3. Dynkin’s identity. Stopping times, strong Markov property, Feller & strong Feller processes. 4. Irreducible Markov processes, ergodic theorem for finite state spaces and in general case. 5. Doob-Doeblin's and Markov-Dobrushin's conditions of ergodicity. 6. Positive & null recurrent, polynomially & exponentially recurrent Markov processes. 7. Coupling method, lemma about three random variables, application to convergence rates. 8. Applications to queueing: Erlang telephone systems, stationary regimes, convergence rates. 9. Piecewise-linear Markov processes, extended Erlang formulae & convergence rates. 10. Applications to some reliability theory problems.

Lecturer

  • AV

    Prof Alexander Veretennikov

    University
    University of Leeds

Bibliography

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Assessment

Attention needed

Assessment information will be available nearer the time.

Files

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Lectures

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