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A Bernstein type inequality and moderate deviations for weakly dependent sequences
Authors:Florence Merlev��de  Magda Peligrad  Emmanuel Rio
Institution:1. Laboratoire de math??matiques, Universit?? Paris Est, UMR 8050 CNRS, Batiment Copernic, 5 Boulevard Descartes, 77435, Champs-Sur-Marne, France
2. Department of Mathematical Sciences, University of Cincinnati, P.O. Box 210025, Cincinnati, OH, 45221-0025, USA
3. Laboratoire de math??matiques, Universit?? de Versailles, UMR 8100 CNRS, Batiment Fermat, 45 Avenue des Etats-Unis, 78035, Versailles, France
Abstract:In this paper we present a Bernstein-type tail inequality for the maximum of partial sums of a weakly dependent sequence of random variables that is not necessarily bounded. The class considered includes geometrically and subgeometrically strongly mixing sequences. The result is then used to derive asymptotic moderate deviation results. Applications are given for classes of Markov chains, iterated Lipschitz models and functions of linear processes with absolutely regular innovations.
Keywords:
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