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deviation bounds for additive functionals of markov processes

Published online by Cambridge University Press:  13 November 2007

Patrick Cattiaux  and
Arnaud Guillin
Patrick Cattiaux
Affiliation:
École Polytechnique, CMAP, 91128 Palaiseau cedex, France, CNRS 756, and Université Paris X Nanterre, équipe MODAL'X, UFR SEGMI, 200 avenue de la République, 92001 Nanterre cedex, France; cattiaux@cmapx.polytechnique.fr
Arnaud Guillin
Affiliation:
Ceremade, Université Paris IX Dauphine, 75775 Paris cedex, France, CNRS 7534; guillin@ceremade.dauphine.fr
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Abstract

In this paper we derive non asymptotic deviation bounds for $${\mathbb P}_\nu (|\frac 1t\int_0^t V(X_s) {\rm d}s - \int V {\rm d} \mu | \geq R)$$ 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.).

Keywords

Deviation inequalitiesfunctional inequalitiesadditive functionals.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 12 , 2008 , pp. 12 - 29
Copyright
© EDP Sciences, SMAI, 2008

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