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Dissertation/Thesis Abstract

Stationary distributions for stochastic delay differential equations with non-negativity constraints
by Kinnally, Michael Sean, Ph.D., University of California, San Diego, 2009, 124; 3355747
Abstract (Summary)

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 focussed 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.

Indexing (document details)
Advisor: Williams, Ruth J.
Commitee: Fitzsimmons, Patrick J., Franceschetti, Massimo, Liu, Jun, Schweinsberg, Jason R.
School: University of California, San Diego
Department: Mathematics
School Location: United States -- California
Source: DAI-B 70/05, Dissertation Abstracts International
Subjects: Mathematics
Keywords: Nonnegativity constraints, Probability, Stationary distributions, Stochastic differential equations, Stochastic processes
Publication Number: 3355747
ISBN: 978-1-109-15068-1
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