# deviation bounds for additive functionals of markov processes

Patrick Cattiaux; Arnaud Guillin

ESAIM: Probability and Statistics (2007)

- 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 (2007): 12-29. <http://eudml.org/doc/104392>.

@article{Cattiaux2007,

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.).
},

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

journal = {ESAIM: Probability and Statistics},

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

language = {eng},

month = {11},

pages = {12-29},

publisher = {EDP Sciences},

title = {deviation bounds for additive functionals of markov processes},

url = {http://eudml.org/doc/104392},

volume = {12},

year = {2007},

}

TY - JOUR

AU - Cattiaux, Patrick

AU - Guillin, Arnaud

TI - deviation bounds for additive functionals of markov processes

JO - ESAIM: Probability and Statistics

DA - 2007/11//

PB - EDP Sciences

VL - 12

SP - 12

EP - 29

AB -
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.).

LA - eng

KW - Deviation inequalities; functional inequalities; additive functionals.; deviation inequalities; additive functionals

UR - http://eudml.org/doc/104392

ER -

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