Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Representation formula for the entropy and functional inequalities

Joseph Lehec

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Abstract

We prove a stochastic formula for the Gaussian relative entropy in the spirit of Borell’s formula for the Laplace transform. As an application, we give simple proofs of a number of functional inequalities.

Résumé

On démontre une formule stochastique pour l’entropie relative par rapport à la Gaussienne, dans le genre de la formule de Borell pour la transformée de Laplace. Cette formule donne des preuves simples d’un certain nombre d’inégalités fonctionnelles.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist. Volume 49, Number 3 (2013), 885-899.

Dates
First available in Project Euclid: 2 July 2013

Permanent link to this document
http://projecteuclid.org/euclid.aihp/1372772648

Digital Object Identifier
doi:10.1214/11-AIHP464

Mathematical Reviews number (MathSciNet)
MR3112438

Zentralblatt MATH identifier
1279.39011

Subjects
Primary: 39B62: Functional inequalities, including subadditivity, convexity, etc. [See also 26A51, 26B25, 26Dxx] 60J65: Brownian motion [See also 58J65]

Keywords
Gaussian measure Entropy Functional inequalities Girsanov’s formula

Citation

Lehec, Joseph. Representation formula for the entropy and functional inequalities. Ann. Inst. H. Poincaré Probab. Statist. 49 (2013), no. 3, 885--899. doi:10.1214/11-AIHP464. http://projecteuclid.org/euclid.aihp/1372772648.


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