Chaotic extensions and the lent particle method for Brownian motion

Nicolas Bouleau , Laurent Denis (1)

1 LMM - Laboratoire Manceau de Mathématiques

In previous works, we have developed a new Malliavin calculus on the Poisson space based on the lent particle formula. The aim of this work is to prove that, on the Wiener space for the standard Ornstein-Uhlenbeck structure, we also have such a formula which permits to calculate easily and intuitively the Malliavin derivative of a functional. Our approach uses chaos extensions associated to stationary processes of rotations of normal martingales.

Mots clés: Malliavin calculus; chaotic extensions; normal martingales AMS MSC 2010: 60H07; 60H15; 60G44; 60G51

Domaines: Probabilités [math.PR]

Nicolas Bouleau, Laurent Denis. Chaotic extensions and the lent particle method for Brownian motion. Electronic Journal of Probability, 2013, 18 (none), ⟨10.1214/ejp.v18-1838⟩. ⟨hal-03687252⟩