Reduced-order modeling of nonlinear singularly perturbed systems driven by wide-band noise

A class of nonlinear singularly perturbed systems driven by wide-band noise is considered. The asymptotic behavior of the slow variables is studied When the fast variables are sufficiently fast (represented by μ → 0) and the wide-band noise is sufficiently wide (represented by ϵ → 0). A reduced-order Markov model to represent the behavior of the slow variables is derived. It is shown that the slow variables converge weakly to the solution of this reduced-order model as ϵ and µ tend to zero. The coefficients of this reduced-order model depend, in general, on the ratio ϵμ. Special cases where the model is independent of ϵ/μ are explored.