On Existence and Uniqueness of Stationary Distributions for Stochastic Delay Differential Equations with Positivity Constraints
Michael S Kinnally, University of California, San Diego
Ruth J. Williams, University of California, San Diego
Abstract
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.
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