Quasi-stationary distributions for absorbing stochastically monotone Markov chains

doi:2016.03.006

Abstract

Abstract: In this paper, we prove some limit theorems for absorbing stochastically monotone Markov chain during its lifetime. The emphases are on the stationary conditional, doubly limiting conditional and limiting conditional mean ratio quasi-stationary distributions. We study the uniqueness and domain of attraction of
three types of quasi-stationary distributions for stochastically monotone Markov chains. A sufficient condition for the uniqueness of the three types of quasi-stationary distributions is given in our main results and under this condition, the unique quasi-stationary distribution attracts all initial distributions. We apply the main results to birth and death processes.

Key words: domain of attraction, quasi-stationary distribution;Markov chain;birth anddeath process

CLC Number:

O211.6

ZHU Yi-Xia. Quasi-stationary distributions for absorbing stochastically monotone Markov chains[J]. Journal of East China Normal University(Natural Sc, 2016, 2016(3): 48-59.

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