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Invariant measures and regularity properties of perturbed Ornstein–Uhlenbeck semigroups

By Abdelhadi Es-Sarhir and Bálint Farkas


AbstractThis 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

Publisher: Elsevier Inc.
Year: 2007
DOI identifier: 10.1016/j.jde.2006.09.022
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