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A convex/log-concave correlation inequality for Gaussian measure and an application to abstract Wiener spaces
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  • Published: 05 July 2004

A convex/log-concave correlation inequality for Gaussian measure and an application to abstract Wiener spaces

  • Gilles Hargé1 

Probability Theory and Related Fields volume 130, pages 415–440 (2004)Cite this article

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Abstract.

This paper deals with a generalization of a result due to Brascamp and Lieb which states that in the space of probabilities with log-concave density with respect to a Gaussian measure on this Gaussian measure is the one which has strongest moments. We show that this theorem remains true if we replace xα by a general convex function. Then, we deduce a correlation inequality for convex functions quite better than the one already known. Finally, we prove results concerning stochastic analysis on abstract Wiener spaces through the notion of approximate limit.

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Authors and Affiliations

  1. Equipe d’analyse et de probabilités, Université d’Evry, rue du père Jarlan, Bat. Maupertuis, 91025, Evry Cedex, France

    Gilles Hargé

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  1. Gilles Hargé
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Correspondence to Gilles Hargé.

Additional information

Mathematics Subject Classification (2000): Primary: 28C20, 60E15, 60H05

Revised version: 20 February 2004

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Hargé, G. A convex/log-concave correlation inequality for Gaussian measure and an application to abstract Wiener spaces. Probab. Theory Relat. Fields 130, 415–440 (2004). https://doi.org/10.1007/s00440-004-0365-8

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  • Received: 20 February 2002

  • Published: 05 July 2004

  • Issue Date: November 2004

  • DOI: https://doi.org/10.1007/s00440-004-0365-8

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Keywords

  • Gaussian measure
  • Optimal transportation
  • Log-concavity
  • Semigroups
  • Stochastic analysis
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