ORNSTEIN-UHLENBECK PROCESS ON A SUBMANIFOLD OF WIENER SPACE

We prove that the symmetric forms defined on finite codimensional submanifolds of the Wiener space are closable. We study the capacities induced by these symmetric forms. In particular, for a finite codimensional submanifold V, we prove the existence of an increasing sequence K(n) of compact sets of V such that the sequence of the capacities of V-K(n) goes to zero when n goes to infinity. After an adaptation of S. Kusuoka's method, this allows to construct a process on the submanifold V.