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.
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