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Sur le théorème de Berry-Esseen pour les suites faiblement dépendantes
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  • Published: June 1996

Sur le théorème de Berry-Esseen pour les suites faiblement dépendantes

About the Berry-Esseen Theorem for weakly dependent sequences

  • Emmanuel Rio1 

Probability Theory and Related Fields volume 104, pages 255–282 (1996)Cite this article

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Résumé

Nous étendons la méthode de démonstration du théorème de Berry-Esseen proposée par Bergström aux suites de variables aléatoires faiblement dépendantes. En particulier, nous montrons que, pour les suites stationnaires de variables aléatoires réelles bornées, la vitesse de convergence dans le théorème limite central en distance de Lévy est de l'ordre den −1/2 dès que la suite (θ p)p>0 des coefficients de mélange uniforme satisfait la condition Σ p>0 pθ p <∞

Abstract

We extend the method of Bergström for the rates of convergence in the central limit theorem to weakly dependent sequences. In particular, we prove that, for stationary and uniformly mixing sequences of real-valued and bounded random variables, the rate of convergence in the central limit theorem is of the order ofn −1/2 as soon as the sequence (θ p)p>0 of uniform mixing coefficients satisfies Σ p>0 pθ p <∞.

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Authors and Affiliations

  1. URA no 0743 CNRS, Université de Paris-Sud, Bât. 425, Mathématique, F-91405, Orsay Cedex, France

    Emmanuel Rio

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  1. Emmanuel Rio
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Rio, E. Sur le théorème de Berry-Esseen pour les suites faiblement dépendantes. Probab. Th. Rel. Fields 104, 255–282 (1996). https://doi.org/10.1007/BF01247840

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  • Received: 17 January 1995

  • Revised: 31 May 1995

  • Issue Date: June 1996

  • DOI: https://doi.org/10.1007/BF01247840

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Mathematics Subject Classifications (1991)

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