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On geometric and algebraic transience for discrete-time Markov chains

Author

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  • Mao, Yong-Hua
  • Song, Yan-Hong

Abstract

General characterizations of ergodic Markov chains have been developed in considerable detail. In this paper, we study the transience for discrete-time Markov chains on general state spaces, including the geometric transience and algebraic transience. Criteria are presented through bounding the modified moment of the first return time and establishing the appropriate drift condition. Moreover, we apply the criteria to the random walk on the half line and the skip-free chain on nonnegative integers.

Suggested Citation

  • Mao, Yong-Hua & Song, Yan-Hong, 2014. "On geometric and algebraic transience for discrete-time Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 124(4), pages 1648-1678.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:4:p:1648-1678
    DOI: 10.1016/j.spa.2013.12.012
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    Cited by:

    1. Song, Yan-Hong, 2016. "Algebraic ergodicity for SDEs driven by Lévy processes," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 108-115.
    2. Yong-Hua Mao & Yan-Hong Song, 2022. "Criteria for Geometric and Algebraic Transience for Discrete-Time Markov Chains," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1974-2008, September.
    3. Phil Pollett, 2022. "Quasi-stationary distributions for queueing and other models," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 241-243, April.

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