Deviation bounds for additive functionals of Markov processes

Cattiaux, Patrick; Guillin, Arnaud

Cattiaux, Patrick; Guillin, Arnaud (2008), Deviation bounds for additive functionals of Markov processes, ESAIM. Probability and Statistics, 12, p. 12-29. http://dx.doi.org/10.1051/ps:2007032

Type

Article accepté pour publication ou publié

Lien vers un document non conservé dans cette base

http://hal.archives-ouvertes.fr/hal-00020035/en/

Date

2008

Nom de la revue

ESAIM. Probability and Statistics

Volume

Éditeur

EDP Sciences

Pages

12-29

Résumé (EN)

In this paper we derive non asymptotic deviation bounds for $$\P_\nu (|\frac 1t \int_0^t V(X_s) ds - \int V d\mu | \geq R)$$ where $X$ is a $\mu$ stationary and ergodic Markov process and $V$ is some $\mu$ integrable function. These bounds are obtained under various moments assumptions for $V$, and various regularity assumptions for $\mu$. Regularity means here that $\mu$ may satisfy various functional inequalities (F-Sobolev, generalized Poincar\'e etc...).

Mots-clés

additive functionals; functional inequalities; Deviation inequalities