Time regularity for generalized Mehler semigroups.

We study continuity and Hölder continuity of t↦Ptf$t\mapsto P_tf$, where Pt$P_t$ is a generalized Mehler semigroup in Cb(X)$C_b(X)$, the space of the continuous and bounded functions from a Banach space X to R$\mathbb {R}$, and f∈Cb(X)$f\in C_b(X)$. The generators L of such semigroups are realizations of a class of differential and pseudo‐differential operators, both in finite and in infinite dimension. Examples of operators L to which this theory is applicable include Ornstein–Uhlenbeck operators with fractional diffusion in finite dimension, and Ornstein–Uhlenbeck operators with associated strong‐Feller semigroups, in infinite dimension. [ABSTRACT FROM AUTHOR]