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Sub-exponential rate of convergence to equilibrium for processes on the half-line

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  • Sarantsev, Andrey

Abstract

A powerful tool for studying long-term convergence of a Markov process to its stationary distribution is a Lyapunov function. In some sense, this is a substitute for eigenfunctions. For a stochastically ordered Markov process on the half-line, Lyapunov functions can be used to easily find explicit rates of convergence. Our earlier research focused on exponential rate of convergence. This note extends these results to slower rates, including power rates, thus improving results of Douc et al. (2009).

Suggested Citation

  • Sarantsev, Andrey, 2021. "Sub-exponential rate of convergence to equilibrium for processes on the half-line," Statistics & Probability Letters, Elsevier, vol. 175(C).
    • Handle: RePEc:eee:stapro:v:175:y:2021:i:c:s0167715221000778
    DOI: 10.1016/j.spl.2021.109115
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    References listed on IDEAS

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    1. Fort, Gersende & Moulines, Eric, 2000. "V-Subgeometric ergodicity for a Hastings-Metropolis algorithm," Statistics & Probability Letters, Elsevier, vol. 49(4), pages 401-410, October.
    2. Sarantsev, Andrey, 2020. "Convergence rate to equilibrium in Wasserstein distance for reflected jump–diffusions," Statistics & Probability Letters, Elsevier, vol. 165(C).
    3. Douc, Randal & Fort, Gersende & Guillin, Arnaud, 2009. "Subgeometric rates of convergence of f-ergodic strong Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 897-923, March.
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    Cited by:

    1. Guodong Pang & Andrey Sarantsev & Yuri Suhov, 2022. "Birth and death processes in interactive random environments," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 269-307, October.

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