Deviation bounds for additive functionals of Markov processes
ESAIM: Probability and Statistics, Tome 12 (2008), pp. 12-29.

In this paper we derive non asymptotic deviation bounds for

ν (|1 t∫ 0 t V(X s )ds-∫Vdμ|≥R)
where X is a μ stationary and ergodic Markov process and V is some μ integrable function. These bounds are obtained under various moments assumptions for V, and various regularity assumptions for μ. Regularity means here that μ may satisfy various functional inequalities (F-Sobolev, generalized Poincaré etc.).

DOI : 10.1051/ps:2007032
Classification : 60F10, 60J25
Mots-clés : deviation inequalities, functional inequalities, additive functionals 
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     title = {Deviation bounds for additive functionals of {Markov} processes},
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Cattiaux, Patrick; Guillin, Arnaud. Deviation bounds for additive functionals of Markov processes. ESAIM: Probability and Statistics, Tome 12 (2008), pp. 12-29. doi : 10.1051/ps:2007032. http://archive.numdam.org/articles/10.1051/ps:2007032/

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