McDaniel, A.; Duman, Ö.; Volpe, G.; Wehr, J. An SDE approximation for stochastic differential delay equations with state-dependent colored noise. (English) Zbl 1356.60091 Markov Process. Relat. Fields 22, No. 3, 595-628 (2016). Summary: 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 T. G. Kurtz and P. Protter [Ann. Probab. 19, No. 3, 1035–1070 (1991; Zbl 0742.60053)]. 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. Cited in 2 Documents MSC: 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 34F05 Ordinary differential equations and systems with randomness Keywords:stochastic differential equations; stochastic differential delay equations; colored noise; noise-induced drift Citations:Zbl 0742.60053 PDFBibTeX XMLCite \textit{A. McDaniel} et al., Markov Process. Relat. Fields 22, No. 3, 595--628 (2016; Zbl 1356.60091) Full Text: arXiv