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Article Dans Une Revue Stochastic Processes and their Applications Année : 2009

Subgeometric rates of convergence of f-ergodic strong Markov processes

Résumé

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

Dates et versions

hal-01314855 , version 1 (12-05-2016)

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Randal Douc, Gersende Fort, Arnaud Guillin. Subgeometric rates of convergence of f-ergodic strong Markov processes. Stochastic Processes and their Applications, 2009, 119 (3), pp.897 - 923. ⟨10.1016/j.spa.2008.03.007⟩. ⟨hal-01314855⟩
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