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Large deviations and related problems for absorbing Markov chains

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  • Chen, Jinwen
  • Deng, Xiaoxue

Abstract

In this paper, large deviations and their connections with several other fundamental topics are investigated for absorbing Markov chains. A variational representation for the Dirichlet principal eigenvalues is given by the large deviation approach. Kingman’s decay parameters and mean ratio quasi-stationary distributions of the chains are also characterized by the large deviation rate function. As an application of these results, we interpret the “stationarity” of mean ratio quasi-stationary distributions via a concrete example. An application to quasi-ergodicity is also discussed.

Suggested Citation

  • Chen, Jinwen & Deng, Xiaoxue, 2013. "Large deviations and related problems for absorbing Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2398-2418.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:6:p:2398-2418
    DOI: 10.1016/j.spa.2013.02.014
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    References listed on IDEAS

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    1. Bolthausen, Erwin & Schmock, Uwe, 1989. "On the maximum entropy principle for uniformly ergodic Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 33(1), pages 1-27, October.
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    Cited by:

    1. He, Guoman & Zhang, Hanjun & Zhu, Yixia, 2019. "On the quasi-ergodic distribution of absorbing Markov processes," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 116-123.

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