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COMPUTABLE STRONGLY ERGODIC RATES OF CONVERGENCE FOR CONTINUOUS-TIME MARKOV CHAINS

Part of: Markov processes

Published online by Cambridge University Press:  01 April 2008

YUANYUAN LIU ,
HANJUN ZHANG  and
YIQIANG ZHAO
YUANYUAN LIU*
Affiliation:
School of Mathematics, Railway Campus, Central South University, Changsha, Hunan, 410075, PR China (email: liuyy@csu.edu.cn)
HANJUN ZHANG
Affiliation:
School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, PR China (email: hjzhang001@gmail.com)
YIQIANG ZHAO
Affiliation:
School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, K1S 5B6, Canada (email: zhao@math.carleton.ca)
*
✉For correspondence; e-mail: liuyy@csu.edu.cn
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Abstract

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In this paper, we investigate computable lower bounds for the best strongly ergodic rate of convergence of the transient probability distribution to the stationary distribution for stochastically monotone continuous-time Markov chains and reversible continuous-time Markov chains, using a drift function and the expectation of the first hitting time on some state. We apply these results to birth–death processes, branching processes and population processes.

Keywords

strong ergodicityconvergence ratebirth and death processbranching processpopulation process

MSC classification

Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Article
Information
The ANZIAM Journal , Volume 49 , Issue 4 , April 2008 , pp. 463 - 478
Copyright
Copyright © Australian Mathematical Society 2008

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