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2013 Chaotic extensions and the lent particle method for Brownian motion
Nicolas Bouleau, Laurent Denis
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Electron. J. Probab. 18: 1-16 (2013). DOI: 10.1214/EJP.v18-1838

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. "Chaotic extensions and the lent particle method for Brownian motion." Electron. J. Probab. 18 1 - 16, 2013. https://doi.org/10.1214/EJP.v18-1838

Information

Accepted: 20 May 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1285.60051
MathSciNet: MR3065866
Digital Object Identifier: 10.1214/EJP.v18-1838

Subjects:
Primary: 60H07
Secondary: 60G44, 60G51, 60H15

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