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

External document link

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

Date

2008

Journal name

ESAIM. Probability and Statistics

Volume

Publisher

EDP Sciences

Pages

12-29

Abstract (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...).

Subjects / Keywords

additive functionals; functional inequalities; Deviation inequalities