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

Published online by Cambridge University Press:  01 April 2008

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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2008

References

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