Stationary solutions of retarded Ornstein–Uhlenbeck processes in Hilbert spaces

In this note, we shall study a class of retarded Langevin equations in infinite-dimensional spaces. An informative description of stationary solutions is given by means of Green operators, Lyapunov equations, the second moment bounds and retarded point spectrum. The covariance operator of the stationary solution is described as a solution of some retarded operator equation.