Chaotic extensions and the lent particle method for Brownian motion
Probability
2012-01-17 v1
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.
Cite
@article{arxiv.1201.3322,
title = {Chaotic extensions and the lent particle method for Brownian motion},
author = {Nicolas Bouleau and Laurent Denis},
journal= {arXiv preprint arXiv:1201.3322},
year = {2012}
}