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 ${¶}_{\nu }\left(|\frac{1}{t}{\int }_{0}^{t}V\left({X}_{s}\right)\mathrm{d}s-\int V\mathrm{d}\mu |\ge R\right)$ 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.).

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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