Stationary solutions of retarded Ornstein-Uhlenbeck processes in Hilbert spaces
The author studies a class of retarded Langevin equations in a separable Hilbert space. He characterizes the existence of an invariant stationary mild solution by means of the covariance operator, Green's operator and the mean square boundedness for the solution starting in zero. Additionally he gives a sufficient existence criterion by the corresponding Lyapunov equation. The covariance operator of a stationary mild solution solution can be described as the solution of some retarded operator equation.
stochastic partial differential equations
scientific article; zbMATH DE number 5348285
scientific article