Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Moderate deviations for stationary sequences of bounded random variables

Jérôme Dedecker, Florence Merlevède, Magda Peligrad, and Sergey Utev

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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.

Résumé

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.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 45, Number 2 (2009), 453-476.

Dates
First available in Project Euclid: 29 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1241024676

Digital Object Identifier
doi:10.1214/08-AIHP169

Mathematical Reviews number (MathSciNet)
MR2521409

Zentralblatt MATH identifier
1172.60005

Subjects
Primary: 60F10: Large deviations 60G10: Stationary processes

Keywords
Moderate deviations Martingale approximation Stationary processes

Citation

Dedecker, Jérôme; Merlevède, Florence; Peligrad, Magda; Utev, Sergey. Moderate deviations for stationary sequences of bounded random variables. Ann. Inst. H. Poincaré Probab. Statist. 45 (2009), no. 2, 453--476. doi:10.1214/08-AIHP169. https://projecteuclid.org/euclid.aihp/1241024676


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