Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
Abstract : We provide a condition for f-ergodicity of strong Markov processes at a subgeometric rate. This condition is couched in terms of a supermartingale property for a functional of the Markov process. Equivalent formulations in terms of a drift inequality on the extended generator and on the resolvent kernel are given. Results related to (f,r)-regularity and to moderate deviation principle for integral (bounded) functional are also derived. Applications to specific processes are considered, including elliptic stochastic differential equation, Langevin diffusions, hypoelliptic stochastic damping Hamiltonian system and storage models.
Subgeometric rates of convergence of f-ergodic strong Markov processes
DOUC R., FORT Gersende, GUILLIN Arnaud
Université de PARIS - DAUPHINE
Place du Maréchal de Lattre De Tassigny - 75775 PARIS CEDEX 16 - FRANCE
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