Subgeometric rates of convergence of f-ergodic strong Markov processes

Guillin, Arnaud; Fort, Gersende; Douc, Randal

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

Publisher

Elsevier

Pages

897-923

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