In this paper we derive non asymptotic deviation bounds for ¶ν(∣t1∫0tV(Xs)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 Poincar\'e etc...)