Some regularity properties of diffusion processes on abstract Wiener space

Diffusion processes on an abstract Wiener space are constructed from fundamental solutions of second-order parabolic equations with variable coefficients. The transition probabilities of such processes are compared with those of the Wiener process, and continuity of sample paths is established. Several operator semigroups associated with the processes are defined (one locally), and some regularity properties of these semigroups are established.