Representation formula for the entropy and functional inequalities
Annales de l'I.H.P. Probabilités et statistiques, Tome 49 (2013) no. 3, pp. 885-899.

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.

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.

DOI : 10.1214/11-AIHP464
Classification : 39B62, 60J65
Mots-clés : gaussian measure, entropy, functional inequalities, Girsanov's formula 
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Lehec, Joseph. Representation formula for the entropy and functional inequalities. Annales de l'I.H.P. Probabilités et statistiques, Tome 49 (2013) no. 3, pp. 885-899. doi : 10.1214/11-AIHP464. http://www.numdam.org/articles/10.1214/11-AIHP464/

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