Volume 12, April 2008
|Page(s)||12 - 29|
|Published online||13 November 2007|
deviation bounds for additive functionals of markov processes
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; email@example.com
2 Ceremade, Université Paris IX Dauphine, 75775 Paris cedex, France, CNRS 7534; firstname.lastname@example.org
Revised: 19 June 2006
Revised: 26 September 2006
In this paper we derive non asymptotic deviation bounds for 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.).
Mathematics Subject Classification: 60F10 / 60J25
Key words: Deviation inequalities / functional inequalities / additive functionals.
© EDP Sciences, SMAI, 2008
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