On Existence and Uniqueness of Stationary Distributions for Stochastic Delay Differential Equations with Positivity 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 positivity 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.
In the Electronic Journal of Probability, Vol. 15 (2010), 409-451. Published on: April 28, 2010. For a copy of a preprint of the Kinnally-Williams paper for personal, scientific, non commercial use, click here for pdf.
For a list of references in the paper with Mathscinet links, click here.
Click here to access a pdf preprint of the article by Hairer, Mattingly and Scheutzow referenced in the Kinnally-Williams paper.
Last updated: April 11, 2010