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.
Mots clés : 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}, pages = {885--899}, publisher = {Gauthier-Villars}, volume = {49}, number = {3}, year = {2013}, doi = {10.1214/11-AIHP464}, mrnumber = {3112438}, zbl = {1279.39011}, language = {en}, url = {http://www.numdam.org/articles/10.1214/11-AIHP464/} }
TY - JOUR AU - Lehec, Joseph TI - Representation formula for the entropy and functional inequalities JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2013 SP - 885 EP - 899 VL - 49 IS - 3 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/11-AIHP464/ DO - 10.1214/11-AIHP464 LA - en ID - AIHPB_2013__49_3_885_0 ER -
%0 Journal Article %A Lehec, Joseph %T Representation formula for the entropy and functional inequalities %J Annales de l'I.H.P. Probabilités et statistiques %D 2013 %P 885-899 %V 49 %N 3 %I Gauthier-Villars %U http://www.numdam.org/articles/10.1214/11-AIHP464/ %R 10.1214/11-AIHP464 %G en %F AIHPB_2013__49_3_885_0
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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