# Deviation bounds for additive functionals of Markov processes

Patrick Cattiaux; Arnaud Guillin

ESAIM: Probability and Statistics (2008)

- Volume: 12, page 12-29
- ISSN: 1292-8100

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topCattiaux, Patrick, and Guillin, Arnaud. "Deviation bounds for additive functionals of Markov processes." ESAIM: Probability and Statistics 12 (2008): 12-29. <http://eudml.org/doc/245164>.

@article{Cattiaux2008,

abstract = {In this paper we derive non asymptotic deviation bounds for\[¶\_\nu (|\frac\{1\}\{t\} \int \_0^t V(X\_s) \{\rm d\}s - \int V \{\rm d\} \mu | \ge R)\]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 Poincaré etc.).},

author = {Cattiaux, Patrick, Guillin, Arnaud},

journal = {ESAIM: Probability and Statistics},

keywords = {deviation inequalities; functional inequalities; additive functionals},

language = {eng},

pages = {12-29},

publisher = {EDP-Sciences},

title = {Deviation bounds for additive functionals of Markov processes},

url = {http://eudml.org/doc/245164},

volume = {12},

year = {2008},

}

TY - JOUR

AU - Cattiaux, Patrick

AU - Guillin, Arnaud

TI - Deviation bounds for additive functionals of Markov processes

JO - ESAIM: Probability and Statistics

PY - 2008

PB - EDP-Sciences

VL - 12

SP - 12

EP - 29

AB - In this paper we derive non asymptotic deviation bounds for\[¶_\nu (|\frac{1}{t} \int _0^t V(X_s) {\rm d}s - \int V {\rm d} \mu | \ge R)\]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 Poincaré etc.).

LA - eng

KW - deviation inequalities; functional inequalities; additive functionals

UR - http://eudml.org/doc/245164

ER -

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