An SDE approximation for stochastic differential delay equations with state-dependent colored noise
Probability
2016-11-02 v3 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1406.7287,
title = {An SDE approximation for stochastic differential delay equations with state-dependent colored noise},
author = {Austin McDaniel and Ozer Duman and Giovanni Volpe and Jan Wehr},
journal= {arXiv preprint arXiv:1406.7287},
year = {2016}
}