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

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.

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.

DOI : https://doi.org/10.1214/11-AIHP464
Classification:  39B62,  60J65
Keywords: gaussian measure, entropy, functional inequalities, Girsanov's formula
@article{AIHPB_2013__49_3_885_0,
     author = {Lehec, Joseph},
     title = {Representation formula for the entropy and functional inequalities},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {49},
     number = {3},
     year = {2013},
     pages = {885-899},
     doi = {10.1214/11-AIHP464},
     zbl = {1279.39011},
     mrnumber = {3112438},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2013__49_3_885_0}
}
Representation formula for the entropy and functional inequalities. Annales de l'I.H.P. Probabilités et statistiques, Volume 49 (2013) no. 3, pp. 885-899. doi : 10.1214/11-AIHP464. http://www.numdam.org/item/AIHPB_2013__49_3_885_0/

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