Gross-Sobolev spaces on path manifolds: uniqueness and intertwining by Ito maps

Conditions are given under which the solution map I of a stochastic differential equation on a Riemannian manifolds M intertwines the differentiation operator d on the path space of M and that of the canonical Wiener space, d(Omega)I* = I* dC(x0) M. A uniqueness property of d on the path space follows. Results are also given for higher derivatives and covariant derivatives. (C) 2003 Academie des sciences. Published by Elsevier SAS. All rights reserved