The structure of entrance laws for time-inhomogeneous Ornstein–Uhlenbeck processes with Lévy noise in Hilbert spaces

This paper is about the structure of all entrance laws (in sense Dynkin) for time-inhomogeneous Ornstein–Uhlenbeck processes with Lévy noise in Hilbert state spaces. We identify extremal finite weak first moments through an explicit formula their Fourier transforms, generalizing corresponding results by Dynkin Wiener and nuclear then prove that arbitrary law can be uniquely represented as integral over extremals. It proved this derived from Dynkin’s seminal work “Sufficient statistics extreme points” Ann. Probab. 1978, which contains a purely measure theoretic generalization classical analytic Krein–Milman Choquet Theorems. As application, we obtain easy uniqueness proof [Formula: see text]-periodic general periodic case. A number further applications to concrete cases are presented.