On Dynamical Systems Perturbed by a Null-Recurrent Fast Motion: The Continuous Coefficient Case with Independent Driving Noises

An ordinary differential equation perturbed by a null-recurrent diffusion will be considered in the case where the averaging type perturbation is strong only when a fast motion is close to the origin. The normal deviations of these solutions from the averaged motion are studied, and a central limit type theorem is proved. The limit process satisfies a linear equation driven by a Brownian motion time changed by the local time of the fast motion.