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Processus empiriques absolument réguliers et entropie universelle
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  • Published: August 1998

Processus empiriques absolument réguliers et entropie universelle

English title: Absolutely regular empirical processes and universal entropy

  • Emmanuel Rio1 

Probability Theory and Related Fields volume 111, pages 585–608 (1998)Cite this article

Abstract.

We extend Pollard's uniform central limit theorem for empirical processes indexed by families of functions ℱ to β-mixing empirical processes. Under some suitable universal entropy conditions on ℱ, we prove a functional central limit theorem for stationary and β-mixing sequences under the minimal sommability condition on the β-mixing coefficients ∑ n β n <∞.

Résumé.

Nous étendons le théorème limite central fonctionnel de Pollard pour les processus empiriques indexés par des familles de fonctions ℱ d'entropie universelle intégrable aux suites d'observations absolument régulières et stationnaires. Sous des conditions d'entropie universelles sur ℱ raisonnables, nous montrons un théorème limite central uniforme pour les suites de variables aléatoires absolument régulières et stationnaires sous la condition minimale de sommabilité des coefficients de β-mélange ∑ n β n <∞.

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Authors and Affiliations

  1. URA no. 0743 CNRS, Université de Paris-Sud, Bât. 425, Mathématique, F-91405 Orsay Cedex France. e-mail: emmanuel.rio@math.u-psud.fr, , , , , , FR

    Emmanuel Rio

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  1. Emmanuel Rio
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Reçu: 21 février 1997 / Version revisée: 24 novembre 1997

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Rio, E. Processus empiriques absolument réguliers et entropie universelle. Probab Theory Relat Fields 111, 585–608 (1998). https://doi.org/10.1007/s004400050179

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  • Issue Date: August 1998

  • DOI: https://doi.org/10.1007/s004400050179

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  • Mathematics Subject Classification (1991): 60F05
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