Approximation of a class of functional differential equations with wideband noise perturbations.

This work focuses on functional differential equations subject to wideband noise perturbations. Modeling using a white noise is often an idealization of the actual physical process, whereas a wideband noise can be easily realized in applications and well approximates a white noise. Using functional derivatives together with the combined perturbed test function methods and martingale techniques, this paper demonstrates that when a small parameter tends to zero, the underlying process converges to a limit that is the solution of a stochastic functional differential equation. To illustrate, an integro-differential system with wideband noise perturbation is examined as an example. Not only are the results interesting from a mathematical point of view, but also they are of utility to a wide range of applications. [ABSTRACT FROM AUTHOR]