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Subgeometric rates of convergence of f-ergodic strong Markov processes

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  • Douc, Randal
  • Fort, Gersende
  • Guillin, Arnaud

Abstract

We provide a condition in terms of a supermartingale property for a functional of the Markov process, which implies (a) f-ergodicity of strong Markov processes at a subgeometric rate, and (b) a moderate deviation principle for an integral (bounded) functional. An equivalent condition in terms of a drift inequality on the extended generator is also given. Results related to (f,r)-regularity of the process, of some skeleton chains and of the resolvent chain are also derived. Applications to specific processes are considered, including elliptic stochastic differential equations, Langevin diffusions, hypoelliptic stochastic damping Hamiltonian systems and storage models.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:3:p:897-923
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    References listed on IDEAS

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    Cited by:

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    4. Guo, Xianping & Liao, Zhong-Wei, 2021. "Estimate the exponential convergence rate of f-ergodicity via spectral gap," Statistics & Probability Letters, Elsevier, vol. 168(C).
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    8. Connor, S.B. & Fort, G., 2009. "State-dependent Foster-Lyapunov criteria for subgeometric convergence of Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 4176-4193, December.
    9. Arapostathis, Ari & Pang, Guodong, 2019. "Infinite horizon asymptotic average optimality for large-scale parallel server networks," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 283-322.

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