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On the quasi-ergodic distribution of absorbing Markov processes

Author

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  • He, Guoman
  • Zhang, Hanjun
  • Zhu, Yixia

Abstract

In this paper, we give a sufficient condition for the existence of a quasi-ergodic distribution for absorbing Markov processes. Using an orthogonal-polynomial approach, we prove that the previous main result is valid for the birth–death process on the nonnegative integers with 0 an absorbing boundary and ∞ an entrance boundary. We also show that the quasi-ergodic distribution is stochastically larger than the unique quasi-stationary distribution in the sense of monotone likelihood-ratio ordering for the birth–death process.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:149:y:2019:i:c:p:116-123
    DOI: 10.1016/j.spl.2019.02.001
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    References listed on IDEAS

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    1. van Doorn, Erik A. & Pollett, Philip K., 2013. "Quasi-stationary distributions for discrete-state models," European Journal of Operational Research, Elsevier, vol. 230(1), pages 1-14.
    2. He, Guoman & Zhang, Hanjun, 2016. "On quasi-ergodic distribution for one-dimensional diffusions," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 175-180.
    3. 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.
    4. Breyer, L. A. & Roberts, G. O., 1999. "A quasi-ergodic theorem for evanescent processes," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 177-186, December.
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    Citations

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    Cited by:

    1. Zhang, Hanjun & Mo, Yongxiang, 2023. "Domain of attraction of quasi-stationary distribution for absorbing Markov processes," Statistics & Probability Letters, Elsevier, vol. 192(C).
    2. He, Guoman & Zhang, Hanjun & Yang, Gang, 2021. "Exponential mixing property for absorbing Markov processes," Statistics & Probability Letters, Elsevier, vol. 179(C).
    3. Oçafrain, William, 2020. "Q-processes and asymptotic properties of Markov processes conditioned not to hit moving boundaries," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3445-3476.

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