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Poisson’s equation for discrete-time single-birth processes

Author

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  • Jiang, Shuxia
  • Liu, Yuanyuan
  • Yao, Shuai

Abstract

We consider Poisson’s equation for discrete-time single-birth processes, and we derive its solutions by solving a linear system of infinitely many equations. We apply the solution of Poisson’s equation to obtain the asymptotic variance. The results are further applied to birth–death processes and the scalar-valued GI/M/1-type Markov chains.

Suggested Citation

  • Jiang, Shuxia & Liu, Yuanyuan & Yao, Shuai, 2014. "Poisson’s equation for discrete-time single-birth processes," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 78-83.
    • Handle: RePEc:eee:stapro:v:85:y:2014:i:c:p:78-83
    DOI: 10.1016/j.spl.2013.11.008
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    References listed on IDEAS

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    1. Sandjai Bhulai & Flora M. Spieksma, 2003. "On the uniqueness of solutions to the Poisson equations for average cost Markov chains with unbounded cost functions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(2), pages 221-236, November.
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    Cited by:

    1. Daly, Fraser, 2024. "On Stein’s method for stochastically monotone single-birth chains," Statistics & Probability Letters, Elsevier, vol. 206(C).
    2. Liu, Jinpeng & Liu, Yuanyuan & Zhao, Yiqiang Q., 2022. "Augmented truncation approximations to the solution of Poisson’s equation for Markov chains," Applied Mathematics and Computation, Elsevier, vol. 414(C).

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