Retarded Stationary Ornstein-Uhlenbeck Processes Driven by Lévy Noise and Operator Self-Decomposability

摘要

A class of Langevin equations driven by Lévy processes with time delays are considered. Sufficient conditions are established to find a unique stationary solution of functional stochastic systems studied. The concept of operator self-decomposability, closely related to the stationary solutions, is generalized to retarded Ornstein-Uhlenbeck processes so as that useful conditions under which random variables with self-decomposability are embedded into a stationary retarded Langevin equations are found.