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

Published online by Cambridge University Press:  14 July 2016

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.

Type
Research Papers
Copyright
© Applied Probability Trust 2006 

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