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May 2009 Moderate deviations for stationary sequences of bounded random variables
Jérôme Dedecker, Florence Merlevède, Magda Peligrad, Sergey Utev
Ann. Inst. H. Poincaré Probab. Statist. 45(2): 453-476 (May 2009). DOI: 10.1214/08-AIHP169

Abstract

In this paper we derive the moderate deviation principle for stationary sequences of bounded random variables under martingale-type conditions. Applications to functions of ϕ-mixing sequences, contracting Markov chains, expanding maps of the interval, and symmetric random walks on the circle are given.

Dans cet article, nous établissons un principe de déviation modérée pour des suites stationnaires de variables aléatoires bornées sous différentes conditions projectives. Nous appliquons ces résultats aux suites ϕ-mélangeantes, à certaines chaînes de Markov contractantes, aux transformations uniformément dilatantes de l’intervalle, ainsi qu’à la marche aléatoire symétrique sur le cercle.

Citation

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Jérôme Dedecker. Florence Merlevède. Magda Peligrad. Sergey Utev. "Moderate deviations for stationary sequences of bounded random variables." Ann. Inst. H. Poincaré Probab. Statist. 45 (2) 453 - 476, May 2009. https://doi.org/10.1214/08-AIHP169

Information

Published: May 2009
First available in Project Euclid: 29 April 2009

zbMATH: 1172.60005
MathSciNet: MR2521409
Digital Object Identifier: 10.1214/08-AIHP169

Subjects:
Primary: 60F10 , 60G10

Keywords: Martingale approximation , Moderate deviations , Stationary processes

Rights: Copyright © 2009 Institut Henri Poincaré

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Vol.45 • No. 2 • May 2009
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