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arXiv · 2012.12797

Time regularity for generalized Mehler semigroups

Alessandra Lunardi
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Abstract

We study continuity and H\"older continuity of $t\mapsto P_tf$, where $P_t$ is a generalized Mehler semigroup in $C_b(X)$, the space of the continuous and bounded functions from a Banach space $X$ to $R$, and $f\in C_b(X)$. 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.

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Alessandra Lunardi. 2020-12-23. Time regularity for generalized Mehler semigroups. https://arxiv.org/abs/2012.12797

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