Invariant measures and regularity properties of perturbed Ornstein–Uhlenbeck semigroups

This paper deals with perturbations of the Ornstein–Uhlenbeck operator on L2-spaces with respect to a Gaussian measure μ. We perturb the generator of the Ornstein–Uhlenbeck semigroup by a certain unbounded, non-linear drift, and show various properties of the perturbed semigroup such as compactness and positivity. Strong Feller property, existence and uniqueness of an invariant measure are discussed as well.