Shifted generalized Mehler semigroups
on White Noise Functionals
Abstract:
We study shifted generalized Mehler semigroups on white noise
functionals. We prove characterizations of invariant (white noise)
distribution and the covariance property for shifted generalized Mehler
semigroups. Also, we prove a Liouville type property of a shifted
generalized Mehler semigroup or its infinitesimal generator.
2010 AMS Mathematics Subject Classification: Primary 60H40; Secondary 47D06, 46F25.
Keywords and phrases: white noise theory, shifted generalized Mehler semigroup,
invariant distribution, covariance property, Liouville type property.