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

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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 
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     author = {Lezaud, Pascal},
     title = {Chernoff and {Berry-Ess\'een} inequalities for {Markov} processes},
     journal = {ESAIM: Probability and Statistics},
     pages = {183--201},
     publisher = {EDP-Sciences},
     volume = {5},
     year = {2001},
     zbl = {0998.60075},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PS_2001__5__183_0/}
}
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Lezaud, Pascal. Chernoff and Berry-Esséen inequalities for Markov processes. ESAIM: Probability and Statistics, Tome 5 (2001), pp. 183-201. http://geodesic.mathdoc.fr/item/PS_2001__5__183_0/