Geodesic
Deviation bounds for additive functionals of Markov processes
ESAIM: Probability and Statistics, Tome 12 (2008), pp. 12-29 Cet article a éte moissonné depuis la source Numdam

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In this paper we derive non asymptotic deviation bounds for

ν (|1 t∫ 0 t V(X s )ds-∫Vdμ|≥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.).

DOI : 10.1051/ps:2007032
Classification : 60F10, 60J25
Keywords: deviation inequalities, functional inequalities, additive functionals 
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     author = {Cattiaux, Patrick and Guillin, Arnaud},
     title = {Deviation bounds for additive functionals of {Markov} processes},
     journal = {ESAIM: Probability and Statistics},
     pages = {12--29},
     year = {2008},
     publisher = {EDP-Sciences},
     volume = {12},
     doi = {10.1051/ps:2007032},
     mrnumber = {2367991},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2007032/}
}
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Cattiaux, Patrick; Guillin, Arnaud. Deviation bounds for additive functionals of Markov processes. ESAIM: Probability and Statistics, Tome 12 (2008), pp. 12-29. doi: 10.1051/ps:2007032

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