Covariant Mehler Semigroups in Hilbert Space

#### D. Applebaum

2007, v.13, Issue 1, 159-168

ABSTRACT

We find necessary and sufficient conditions for a generalised Mehler semigroup to be covariant under the action of a locally compact group. These are then applied to implement "noise reduction" for Hilbert-space valued Ornstein - Uhlenbeck processes driven by Levy processes.

Keywords: Mehler semigroup,Levy process,Ornstein - Uhlenbeckprocess,$G$-covariance