A differential delay equation with wideband noise perturbations

A differential delay equation with a small parameter and random noise perturbations is considered in this paper. Asymptotic properties are developed. The martingale averaging techniques are adopted to treat our problem, and the method of weak convergence is employed. The random fluctuation is assumed to be of the wideband noise type, which is quite realistic for various applications. It is shown that as [var epsilon] --> 0, the underlying process converges weakly to a random process which satisfies a stochastic differential delay equation.