| Abstract: | The Ito formula is extended to the tempered distributions "evaluated" on the trajectories of a nondegenerate Ito process in the sense of P. Malliavin. To do this the Ito integral is extended to vector-valued adapted distributions on Wiener space. Also a Galerkin type approximation using the Skorohod integral or the divergence operator is given for the diffusion processes. At the final section we give a sufficient condition for the existence of a smooth density for the filtering of nonlinear diffusions with the help of the techniques of the Malliavin calculus and the theory of nuclear spaces. |
