Fractional Stability of Diffusion Approximation for Random Differential Equations

Abstract

We consider the systems of random differential equations. The coefficients of the equations depend on a small parameter. The first equation, “slow” component, Ordinary Differential Equation (ODE), has unbounded highly oscillating in space variable coefficients and random perturbations, which are described by the second equation, “fast” component, Stochastic Differential Equation (SDE) with periodic coefficients. Sufficient conditions for weak convergence as small parameter goes to zero of the solutions of the “slow” components to the certain stochastic process are given.