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Subgeometric rates of convergence of f-ergodic strong Markov processes

Guillin, Arnaud; Fort, Gersende; Douc, Randal (2009), Subgeometric rates of convergence of f-ergodic strong Markov processes, Stochastic Processes and their Applications, 119, 3, p. 897-923. http://dx.doi.org/10.1016/j.spa.2008.03.007

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00077681/en/
Date
2009
Journal name
Stochastic Processes and their Applications
Volume
119
Number
3
Publisher
Elsevier
Pages
897-923
Publication identifier
http://dx.doi.org/10.1016/j.spa.2008.03.007
Metadata
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Author(s)
Guillin, Arnaud
Fort, Gersende cc
Douc, Randal
Abstract (EN)
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.
Subjects / Keywords
storage models.; hypoelliptic diffusions; Langevin diffusions; moderate deviations; resolvent; Foster's criterion; regularity; Subgeometric ergodicity

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