Chernoff and Berry-Esséen inequalities for Markov processes
ESAIM: Probability and Statistics, Volume 5  (2001), p. 183-201

In this paper, we develop bounds on the distribution function of the empirical mean for general ergodic Markov processes having a spectral gap. Our approach is based on the perturbation theory for linear operators, following the technique introduced by Gillman.

Classification:  60F10
Keywords: Markov process, Chernoff bound, Berry-Esséen, eigenvalues, perturbation theory 
@article{PS_2001__5__183_0,
     author = {Lezaud, Pascal},
     title = {Chernoff and Berry-Ess\'een inequalities for Markov processes},
     journal = {ESAIM: Probability and Statistics},
     publisher = {EDP-Sciences},
     volume = {5},
     year = {2001},
     pages = {183-201},
     zbl = {0998.60075},
     language = {en},
     url = {http://www.numdam.org/item/PS_2001__5__183_0}
}

Lezaud, Pascal. Chernoff and Berry-Esséen inequalities for Markov processes. ESAIM: Probability and Statistics, Volume 5 (2001) , pp. 183-201. http://www.numdam.org/item/PS_2001__5__183_0/

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