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Chernoff and Berry–Esséen inequalities for Markov processes

Published online by Cambridge University Press:  15 August 2002

Pascal Lezaud
Pascal Lezaud*
Affiliation:
Centre d'Études de la Navigation Aérienne, 31055 Toulouse Cedex, France; pascal.lezaud@cena.fr. Université Paul Sabatier, 31055 Toulouse Cedex, France.
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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.

Keywords

Markov processChernoff boundBerry–Esséeneigenvaluesperturbation theory.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 5 , 2001 , pp. 183 - 201
Copyright
© EDP Sciences, SMAI, 2001

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