Existence of invariant measures of diffusions on an abstract Wiener space (Q1098177)

We establish the existence of an invariant measure for a diffusion on an abstract Wiener space (B,H,\(\mu)\), B being a Banach space, H being a Hilbert space and \(\mu\) being the Wiener measure. Here we consider a diffusion generated by an operator of the form \(A=2^{-1}L+b\), L being the Ornstein-Uhlenbeck operator and b being a bounded first order differential operator. We obtain an invariant measure by solving the equation \(A^*\rho =0\) where \(A^*\) is the dual operator in \(L^ 2(d\mu)\). Moreover we obtain a condition for the symmetry of its semigroup.