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Chaotic extensions and the lent particle method for Brownian motion

2012/01/16 by Nicolas Bouleau, Bouleau, Nicolas, Laurent Denis +1
Mathematics · #60G44 #60G51 #60H07 #60H15 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G44 #msc:60G51 #msc:60H07 #msc:60H15

paper · pdf · doi:10.48550/arxiv.1201.3322

arxiv created 2012/01/16 · arxiv updated 2012/01/17

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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