Perturbation for a class of transition semigroups on the Hölder space Cθ b,loc(H) ✩

We prove a perturbation result for the Ornstein–Uhlenbeck generator on the Hölder space Cθ b,loc(H), H is a separable Hilbert space. As a consequence we obtain the existence of transition semigroups and the solution of elliptic problems associated to stochastic differential equations with non-linear drifts.  2005 Elsevier Inc. All rights reserved