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Criteria for Geometric and Algebraic Transience for Discrete-Time Markov Chains

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  • Yong-Hua Mao

    (Ministry of Education)

  • Yan-Hong Song

    (Zhongnan University of Economics and Law)

Abstract

We present new criteria for geometric and algebraic transience for discrete-time transient Markov chains on general state spaces, based on the moment of the last exit time, the modified moment of the first return time and the drift condition for the transition kernel. These criteria turn out to be more convenient to use, supplementing and extending conditions introduced by Mao and Song [Stochastic Process. Appl. 124 (2014) 1648-1678]. Several applications are presented including discrete queueing Markov chains, Galton–Watson branching processes, downwardly skip-free chains, unrestricted random walks and autoregressive models of order one.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:3:d:10.1007_s10959-021-01105-5
    DOI: 10.1007/s10959-021-01105-5
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    References listed on IDEAS

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    1. Nikola Sandrić, 2016. "Ergodic Property of Stable-Like Markov Chains," Journal of Theoretical Probability, Springer, vol. 29(2), pages 459-490, June.
    2. 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.
    3. Nummelin, Esa & Tuominen, Pekka, 1983. "The rate of convergence in Orey's theorem for Harris recurrent Markov chains with applications to renewal theory," Stochastic Processes and their Applications, Elsevier, vol. 15(3), pages 295-311, August.
    4. Wei, C. Z. & Winnicki, J., 1989. "Some asymptotic results for the branching process with immigration," Stochastic Processes and their Applications, Elsevier, vol. 31(2), pages 261-282, April.
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