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Deviation bounds for additive functionals of Markov processes

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Date
2008
Link to item file
http://hal.archives-ouvertes.fr/hal-00020035/en/
Dewey
Probabilités et mathématiques appliquées
Sujet
additive functionals; functional inequalities; Deviation inequalities
Journal issue
ESAIM. Probability and Statistics
Volume
12
Publication date
2008
Article pages
12-29
Publisher
EDP Sciences
DOI
http://dx.doi.org/10.1051/ps:2007032
URI
https://basepub.dauphine.fr/handle/123456789/3459
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Cattiaux, Patrick
Guillin, Arnaud
Type
Article accepté pour publication ou publié
Abstract (EN)
In this paper we derive non asymptotic deviation bounds for $$\P_\nu (|\frac 1t \int_0^t V(X_s) ds - \int V d\mu | \geq R)$$ where $X$ is a $\mu$ stationary and ergodic Markov process and $V$ is some $\mu$ integrable function. These bounds are obtained under various moments assumptions for $V$, and various regularity assumptions for $\mu$. Regularity means here that $\mu$ may satisfy various functional inequalities (F-Sobolev, generalized Poincar\'e etc...).

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