Ergodicity for the $GI/G/1$-type Markov Chain

YongHua Mao; Yongming Tai; Yiqiang Q. Zhao; Jiezhong Zou

Ergodicity for the $GI/G/1$-type Markov Chain

Probability 2012-08-28 v1

Authors: YongHua Mao , Yongming Tai , Yiqiang Q. Zhao , Jiezhong Zou

Abstract

Ergodicity is a fundamental issue for a stochastic process. In this paper, we refine results on ergodicity for a general type of Markov chain to a specific type or the $GI/G/1$ -type Markov chain, which has many interesting and important applications in various areas. It is of interest to obtain conditions in terms of system parameters or the given information about the process, under which the chain has various ergodic properties. Specifically, we provide necessary and sufficient conditions for geometric, strong and polynomial ergodicity, respectively.

Keywords

markov chain markov processes ergodic theory

Cite

@article{arxiv.1208.5225,
  title  = {Ergodicity for the $GI/G/1$-type Markov Chain},
  author = {YongHua Mao and Yongming Tai and Yiqiang Q. Zhao and Jiezhong Zou},
  journal= {arXiv preprint arXiv:1208.5225},
  year   = {2012}
}

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16 pages

Ergodicity for the $GI/G/1$-type Markov Chain

Abstract

Keywords

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