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Exponential ergodicity for single-birth processes

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Yong-Hua Mao  and
Yu-Hui Zhang
Yong-Hua Mao*
Affiliation:
Beijing Normal University
Yu-Hui Zhang*
Affiliation:
Beijing Normal University
*
∗ Postal address: Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China
∗ Postal address: Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China
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Abstract

An explicit, computable, and sufficient condition for exponential ergodicity of single-birth processes is presented. The corresponding criterion for birth–death processes is proved using a new method. As an application, some sufficient conditions are obtained for exponential ergodicity of an extended class of continuous-time branching processes and of multidimensional Q-processes, by comparison methods.

Keywords

Exponentially ergodicsingle-birth processbirth–death process

MSC classification

Primary: 60J25: Continuous-time Markov processes on general state spaces 60J75: Jump processes 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 4 , December 2004 , pp. 1022 - 1032
Copyright
Copyright © Applied Probability Trust 2004 

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