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2010 On Existence and Uniqueness of Stationary Distributions for Stochastic Delay Differential Equations with Positivity Constraints
Michael Kinnally, Ruth Williams
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Electron. J. Probab. 15: 409-451 (2010). DOI: 10.1214/EJP.v15-756

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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Michael Kinnally. Ruth Williams. "On Existence and Uniqueness of Stationary Distributions for Stochastic Delay Differential Equations with Positivity Constraints." Electron. J. Probab. 15 409 - 451, 2010. https://doi.org/10.1214/EJP.v15-756

Information

Accepted: 28 April 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1227.34081
MathSciNet: MR2639731
Digital Object Identifier: 10.1214/EJP.v15-756

Subjects:
Primary: 34K50
Secondary: 37H10, 60H10, 60J25, 93E15

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Vol.15 • 2010
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