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General


This course is part of the MAGIC core.

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.

Semester

Autumn 2017 (Monday, October 9 to Friday, December 15)

Timetable

  • Thu 10:05 - 10:55
  • Fri 10:05 - 10:55

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


Alexander Veretennikov
Email A.Veretennikov@leeds.ac.uk
Phone (0113) 3435183
Photo of Alexander Veretennikov


Students


Photo of Duc Lam Duong
Duc Lam Duong
(Sussex)
Photo of Raffaele Grande
Raffaele Grande
(Cardiff)
Photo of Ozkan Karabacak
Ozkan Karabacak
(Exeter)


Bibliography


Stochastic Processes and ModelsStirzaker
Markov Processes: Characterization and ConvergenceEthier and Kurtz
A course in the theory of stochastic processesVent︠t︡selʹ and Wentzell
Markov Models & OptimizationDavis


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