The paper is concerned with one-dimensional two-sided Ornstein-Uhlenbeck type processes with delay or anticipation. We prove existence and uniqueness requiring almost sure boundedness on the left half-axis in case of delay and almost sure boundedness on the right half-axis in case of anticipation. For those stochastic processes $(X,P_{ \mu})$ we calculate the Radon-Nikodym density under time shift of trajectories, $P_{ \mu}(dX_{ \cdot -t})/P_{ \mu}(dX)$, $t\in { \Bbb R}$.
Categories: math.PR