Chaotic extensions and the lent particle method for Brownian motion

Nicolas Bouleau; Laurent Denis

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arXiv · 1201.3322

Chaotic extensions and the lent particle method for Brownian motion

Nicolas Bouleau·Laurent Denis

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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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Nicolas Bouleau, Laurent Denis. 2012-01-16. Chaotic extensions and the lent particle method for Brownian motion. https://arxiv.org/abs/1201.3322

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