An SDE approximation for stochastic differential delay equations with state-dependent colored noise
Date
2016-11
Authors
McDaniel, A.
Duman, Ö.
Volpe, G.
Wehr, J.
Editor(s)
Advisor
Supervisor
Co-Advisor
Co-Supervisor
Instructor
Source Title
Markov Process and Related Fields
Print ISSN
1024-2953
Electronic ISSN
Publisher
Polymat Publishing
Volume
22
Issue
3
Pages
595 - 628
Language
English
Type
Journal Title
Journal ISSN
Volume Title
Series
Abstract
We consider a general multidimensional stochastic differential delay equation (SDDE) with state-dependent colored noises. We approximate it by a stochastic differential equation (SDE) system and calculate its limit as the time delays and the correlation times of the noises go to zero. The main result is proven using a theorem about convergence of stochastic integrals by Kurtz and Protter. It formalizes and extends a result that has been obtained in the analysis of a noisy electrical circuit with delayed state-dependent noise, and may be used as a working SDE approximation of an SDDE modeling a real system where noises are correlated in time and whose response to noise sources depends on the system's state at a previous time.