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perturbation theory.

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Chernoff and Berry–Esséen inequalitiesfor Markov processes
Pascal Lezaud
Journal:

ESAIM: Probability and Statistics / Volume 5 / 2001

Published online by Cambridge University Press:

15 August 2002, pp. 183-201

Print publication:

2001
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In this paper, we develop bounds on the distribution function of the empiricalmean for general ergodic Markov processes having a spectral gap. Our approach isbased on the perturbation theory for linear operators, following the techniqueintroduced by Gillman.