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.
"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