On Existence and Uniqueness of Stationary Distributions for Stochastic Delay Differential Equations with Non-Negativity Constraints

On Existence and Uniqueness of Stationary Distributions for Stochastic Delay Differential Equations with Non-Negativity Constraints
M. S. Kinnally and R. J. Williams
Deterministic dynamic models with delayed feedback and state constraints arise in a variety of applications in science and engineering. There is interest in understanding what effect noise has on the behavior of such models. 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 for such equations. The results are applied to an example from Internet rate control and a simple biochemical reaction system.

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Last updated: August 17, 2009