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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


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.


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

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

Keywords: chaotic extensions , Malliavin calculus , Normal martingales

Vol.18 • 2013
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