Explicit estimate for convergence rates of continuous time markov chains (I)

HOU Zhenting; ZHANG Zhuo; YAN Zhenhai

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Explicit estimate for convergence rates of continuous time markov chains (I)

HOU Zhenting * #,ZHANG Zhuo,YAN Zhenhai

School of mathematics and statistics, Central South University, Changsha 410075

*Correspondence author

#Submitted by

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Funding: Specialized Research Fund for the Doctoral Program of Higher Education（No.20130162110070）

Opened online:23 May 2017

Accepted by: none

Citation: HOU Zhenting,ZHANG Zhuo,YAN Zhenhai.Explicit estimate for convergence rates of continuous time markov chains (I) [OL]. [23 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4734375

justifying In this paper, we give explicit estimate on the rate of convergence of the transition probabilities to the stationary distribution for a class of exponential ergodic Markov chains. Our results are different from earlier estimates using coupling theory and from estimates using stochastically monotone. The estimates show a noticeable improvement on existing results if Markov chains contain instantaneous state or nonconservative state. The method of proof uses existing result of discrete time Markov chain, together with $h-$ skeleton. We apply this results, Ray-Knight compactification and $mbox{It}hat{o}$ excursion theory to two examples: a class of singular Markov chains and Kolmogorov matrix. In addition, we apply the Ray-Knight compactification, $mbox{It}hat{o}$ excursion theory and explicit estimate for convergence rates of continuous time markov chains to two examples: a class of singular Markov chains and Kolmogorovmatrix.

Keywords:exponential ergodicity; Markov chain; exponential ergodicity; Ray-Knight compactification; Poisson point process

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