Subgeometric rates of convergence of f-ergodic strong Markov processes

Randal Douc, Gersende Fort and Arnaud Guillin

Stochastic Processes and their Applications, 2009, vol. 119, issue 3, 897-923

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.

Keywords: Subgeometric; ergodicity; Regularity; Foster's; criterion; Resolvent; Moderate; deviations; Langevin; diffusions; Hypoelliptic; diffusions; Storage; models (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (9)

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