Deviation bounds for additive functionals of Markov processes
ESAIM: Probability and Statistics, Volume 12  (2008), p. 12-29

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 : https://doi.org/10.1051/ps:2007032
Classification:  60F10,  60J25
Keywords: deviation inequalities, functional inequalities, additive functionals
@article{PS_2008__12__12_0,
     author = {Cattiaux, Patrick and Guillin, Arnaud},
     title = {Deviation bounds for additive functionals of Markov processes},
     journal = {ESAIM: Probability and Statistics},
     publisher = {EDP-Sciences},
     volume = {12},
     year = {2008},
     pages = {12-29},
     doi = {10.1051/ps:2007032},
     zbl = {pre05216895},
     mrnumber = {2367991},
     language = {en},
     url = {http://www.numdam.org/item/PS_2008__12__12_0}
}
Cattiaux, Patrick; Guillin, Arnaud. Deviation bounds for additive functionals of Markov processes. ESAIM: Probability and Statistics, Volume 12 (2008) , pp. 12-29. doi : 10.1051/ps:2007032. http://www.numdam.org/item/PS_2008__12__12_0/

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