A stochastic formula for the entropy and applications

Joseph Lehec (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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 unified and short proofs of various well known inequalities.

Mots clés: Entropy; Girsanov transform; Functional inequalities

Domaines: Probabilités [math.PR]

Joseph Lehec. A stochastic formula for the entropy and applications. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2013, 49 (3), pp.885-899. ⟨10.1214/11-AIHP464⟩. ⟨hal-00534442⟩