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A quasi-ergodic theorem for evanescent processes

Author

Listed:
  • Breyer, L. A.
  • Roberts, G. O.

Abstract

We prove a conditioned version of the ergodic theorem for Markov processes, which we call a quasi-ergodic theorem. We also prove a convergence result for conditioned processes as the conditioning event becomes rarer.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:84:y:1999:i:2:p:177-186
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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 & Zhu, Yixia, 2019. "On the quasi-ergodic distribution of absorbing Markov processes," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 116-123.
    3. Castro, Matheus M. & Lamb, Jeroen S.W. & Olicón-Méndez, Guillermo & Rasmussen, Martin, 2024. "Existence and uniqueness of quasi-stationary and quasi-ergodic measures for absorbing Markov chains: A Banach lattice approach," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    4. He, Guoman & Zhang, Hanjun & Yang, Gang, 2021. "Exponential mixing property for absorbing Markov processes," Statistics & Probability Letters, Elsevier, vol. 179(C).
    5. 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.
    6. He, Guoman & Zhang, Hanjun, 2016. "On quasi-ergodic distribution for one-dimensional diffusions," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 175-180.
    7. Daehong Kim & Takara Tagawa, 2025. "Quasi-Ergodic Limits for Moments of Jumps Under Absorbing Stable Processes," Journal of Theoretical Probability, Springer, vol. 38(1), pages 1-19, March.

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