Chaotic extensions and the lent particle method for Brownian motion

Nicolas Bouleau (École des Ponts ParisTech)
Laurent Denis (University of Évry)

Abstract


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.

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Pages: 1-16

Publication Date: May 20, 2013

DOI: 10.1214/EJP.v18-1838

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