  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.
