Stationary distributions for stochastic delay differential equations with non-negativity constraints
Deterministic dynamic models with delayed feedback and state constraints arise in a variety of applications in science and engineering. Much of the analysis of such deterministic models has focused on stability analysis of equilibrium points. There is interest in understanding what effect noise has on the behavior of such systems. Here we consider a multidimensional stochastic delay differential equation with normal reflection as a noisy analogue of a deterministic system with delayed feedback and non-negativity constraints. We obtain sufficient conditions for existence and uniqueness of stationary distributions. The results are applied to examples from Internet rate control and biochemical reaction systems.