| Issue |
ESAIM: PS
Volume 12, April 2008
|
|
|---|---|---|
| Page(s) | 12 - 29 | |
| DOI | https://doi.org/10.1051/ps:2007032 | |
| Published online | 13 November 2007 | |
deviation bounds for additive functionals of markov processes
1
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
2
Ceremade, Université Paris IX Dauphine, 75775 Paris cedex, France, CNRS 7534; guillin@ceremade.dauphine.fr
Received:
13
March
2006
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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