PUB - Publikationen an der Universität Bielefeld

In this paper we solve the Kolmogorov equation and, as a consequence, the martingale problem corresponding to a stochastic differential equation of type dX(t) = AX(t) dt + b(X-t) dt + dY(t), on a Hilbert space E, where (Y-t)(tgreater than or equal to0) is a Levy process on E, A generates a C-0-semigroup on E and b : E --> E. Our main point is to allow unbounded A and also singular (in particular, non-continuous) b. Our approach is based on perturbation theory of C-0-semigroups, which we apply to generalized Mehler semigroups considered on L-2(mu), where mu is their respective invariant measure. We apply our results, in particular, to stochastic heat equations with Levy noise and singular drift.