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Sur l'équivalence de certaines mesures produit
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  • Published: March 1994

Sur l'équivalence de certaines mesures produit

  • X. Fernique1 

Probability Theory and Related Fields volume 98, pages 77–90 (1994)Cite this article

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Sommaire

SoitG={g k ,k∈N} une suite de variables aléatoires gaussiennes centrées réduites et indépendantes; soit de plusY={y k ,k∈N} une suite indépendante deG de variables aléatoires indépendantes. On étudie à quelles conditions la loi deG+Y est équivalente à celle deG. On utilise pour cela les lois zéro-un vérifiées parG en analysant leurs effets, maximaux sur la loi deY.

Summary

LetG={g k ,k∈N} be a sequence of independent Gaussian centred reduced random variables; let moreoverY={y k ,k∈N} be a sequence independent ofG of independent random variables: For obtaining conditions characterizing the equivalence of the distributions ofG andG+Y, we use the zero-one laws verified byG, first for the convergence of the series ∑σ k g k orσ k (g 2 k −a k ), secundly for the asymptotic behavior of the sequence {g k ,k∈N} and we analyze their maximal effects on the distribution ofY.

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Références

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Authors and Affiliations

  1. Institut de Recherche Mathématique Avancée, Université Louis Pasteur et C.N.R.S., 7, rue René Descartes, F-67084, Strasbourg Cédex, France

    X. Fernique

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  1. X. Fernique
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Fernique, X. Sur l'équivalence de certaines mesures produit. Probab. Th. Rel. Fields 98, 77–90 (1994). https://doi.org/10.1007/BF01311349

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  • Received: 09 June 1992

  • Revised: 08 June 1993

  • Issue Date: March 1994

  • DOI: https://doi.org/10.1007/BF01311349

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Mathematics Subject Classifications (1991)

  • 60G30
  • 60F20
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