Subgeometric rates of convergence of f-ergodic strong Markov processes |
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Authors: | Randal Douc Gersende Fort Arnaud Guillin |
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Affiliation: | 1. CMAP, Ecole Polytechnique, 91128 Palaiseau Cedex, France;2. CNRS/LTCI, 46 rue Barrault, 75634 Paris Cedex 13, France;3. Ecole Centrale Marseille and LATP, CNRS UMR 6632, 39 rue Joliot Curie, 13453 Marseille Cedex 13, France |
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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. |
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Keywords: | primary, 60J25, 37A25 secondary, 60F10, 60J35, 60J60 |
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