Abstract
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 Ω I ∗= I ∗ d C x 0 M . A uniqueness property of d on the path space follows. Results are also given for higher derivatives and covariant derivatives. To cite this article: K.D. Elworthy, X.-M. Li, C. R. Acad. Sci. Paris, Ser. I 337 (2003).
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