Kolmogorov equations in Hilbert spaces with application to essential self-adjointness of symmetric diffusion operators (Q1568368)

A Kolmogorov equation is considered for a semilinear stochastic evolution equation and is defined as mild solution. The existence and uniqueness of a classical solution is proved for the Kolmogorov equation by transition semigroup (Theorem 2.1). There are also given sufficient conditions so that the symmetric Kolmogorov-type operator is essentially selfadjoint (Theorems 3.2, 3.3).