  We present a new path integral method to analyze stochastically perturbed
ordinary differential equations with multiple time scales. The objective of
this method is to derive from the original system a new stochastic differential
equation describing the system's evolution on slow time scales. For this
purpose, we start from the corresponding path integral representation of the
stochastic system and apply a multi-scale expansion to the associated path
integral kernel of the corresponding Lagrangian. As a concrete example, we
apply this expansion to a system that arises in the study of random dispersion
fluctuations in dispersion-managed fiber optic communications. Moreover, we
show that, for this particular example, the new path integration method yields
the same result at leading order as an asymptotic expansion of the associated
Fokker-Planck equation.
