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Several Types of Ergodicity for M/G/1-Type Markov Chains and Markov Processes

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Yuanyuan Liu  and
Zhenting Hou
Yuanyuan Liu*
Affiliation:
Central South University, Changsha
Zhenting Hou*
Affiliation:
Central South University, Changsha
*
∗ Postal address: School of Mathematics, Central South University, Changsha, Hunan, 410075, P. R. China.
∗ Postal address: School of Mathematics, Central South University, Changsha, Hunan, 410075, P. R. China.
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Abstract

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In this paper we study polynomial and geometric (exponential) ergodicity for M/G/1-type Markov chains and Markov processes. First, practical criteria for M/G/1-type Markov chains are obtained by analyzing the generating function of the first return probability to level 0. Then the corresponding criteria for M/G/1-type Markov processes are given, using their h-approximation chains. Our method yields the radius of convergence of the generating function of the first return probability, which is very important in obtaining explicit bounds on geometric (exponential) convergence rates. Our results are illustrated, in the final section, in some examples.

Keywords

Markov chainMarkov processpolynomial ergodicitygeometric ergodicitystrong ergodicity

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 1 , March 2006 , pp. 141 - 158
Copyright
© Applied Probability Trust 2006 

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