Deviation bounds for additive functionals of Markov process

2006/03/01 by Patrick Cattiaux, Arnaud Guillin, Cattiaux, Patrick +1
Mathematics · #60F10 #60J25 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60F10 #msc:60J25

paper · pdf · doi:10.48550/arxiv.math/0603021

arxiv created 2006/03/01 · arxiv updated 2009/12/01

Abstract

In this paper we derive non asymptotic deviation bounds for ¶_ν(|\frac 1t ∫₀^t V(X_s) ds - ∫ V dμ| ≥ 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...).

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