Chernoff and Berry-Esséen inequalities for Markov Processes

Abstract : 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.
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Pascal Lezaud. Chernoff and Berry-Esséen inequalities for Markov Processes. ESAIM: Probability and Statistics, EDP Sciences, 2001, 5, pp 183-201. ⟨10.1051/ps:2001108⟩. ⟨hal-00940906⟩

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