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Existence and uniqueness of quasi-stationary and quasi-ergodic measures for absorbing Markov chains: A Banach lattice approach

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  • Castro, Matheus M.
  • Lamb, Jeroen S.W.
  • Olicón-Méndez, Guillermo
  • Rasmussen, Martin

Abstract

We establish the existence and uniqueness of quasi-stationary and quasi-ergodic measures for almost surely absorbed discrete-time Markov chains under weak conditions. We obtain our results by exploiting Banach lattice properties of transition functions under natural regularity assumptions.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:spapps:v:173:y:2024:i:c:s030441492400070x
    DOI: 10.1016/j.spa.2024.104364
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    References listed on IDEAS

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    1. Günter Hinrichs & Martin Kolb & Vitali Wachtel, 2020. "Persistence of One-Dimensional AR(1)-Sequences," Journal of Theoretical Probability, Springer, vol. 33(1), pages 65-102, March.
    2. Michel Benaïm & Nicolas Champagnat & William Oçafrain & Denis Villemonais, 2023. "Transcritical Bifurcation for the Conditional Distribution of a Diffusion Process," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1555-1571, September.
    3. Haas, Bénédicte & Rivero, Víctor, 2012. "Quasi-stationary distributions and Yaglom limits of self-similar Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 122(12), pages 4054-4095.
    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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