XXXI: 05, 54-61, LNM 1655 (1997)
FANG, Shizan;
FRANCHI, Jacques
A differentiable isomorphism between Wiener space and path group (
Malliavin's calculus)
The Itô map $I$ is known to realize a measurable isomorphism between Wiener space $W$ and the group ${\cal P}$ of paths with values in a Riemannian manifold. Here, the pullback $I^{*}$ is shown to be a diffeomorphism (in the sense of Malliavin derivatives) between the exterior algebras $\Lambda (W)$ and $\Lambda ({\cal P})$. This allows to transfer the Weitzenböck-Shigekawa identity from $\Lambda (W)$ to $\Lambda ({\cal P})$, yielding for example the de~Rham-Hodge-Kodaira decomposition on ${\cal P}$
Keywords: Wiener space,
Path group,
Brownian motion in a manifold,
Differential formsNature: Original
Retrieve article from Numdam
