On processes of ornstein-uhlenbeck type in hilbert space

Abstract

A process fo Ornstein-Uhlenbeck type is a mild solution of the stochastic differential system in Hilbert space dXt=AX t dt+dZ t, where A generates a semigroup of operators and Z tis a process with homogeneous independent increments. The explicit integral formula for the process of O-U type is given. The main purpose is to study stationary distributions for such processes. Sufficient and necessary conditions for existence and characterization are given. The difference between finite and infinite dimensional cases is illustrated by examples