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. 
Zsolt Pajor-Gyulai and Michael Salins
math.PR