Ornstein-Uhlenbeck semigroups in infinite dimension.

Abstract

This is a survey paper about Ornstein-Uhlenbeck semigroups in infinite dimension and their generators. We start from the classical Ornstein-Uhlenbeck semigroup on Wiener spaces and then discuss the general case in Hilbert spaces. Finally, we present some results for Ornstein-Uhlenbeck semigroups on Banach spaces. This article is part of the theme issue 'Semigroup applications everywhere'.