Deviation bounds for additive functionals of Markov processes
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
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00020035/en/
Journal nameESAIM. Probability and Statistics
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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 / Keywordsadditive functionals; functional inequalities; Deviation inequalities
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