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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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    Cited by:

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