English

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.

Keywords

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}
}
R2 v1 2026-06-21T20:05:14.996Z