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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 43, Fasc. 2,
pages 185 - 205
DOI: 10.37190/0208-4147.00123
Published online 6.2.2024
 

Shifted generalized Mehler semigroups on White Noise Functionals

Un Cig
Mi Ra Lee

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.

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