On averaging principle for diffusion processes with null-recurrent fast component

An averaging principle is proved for diffusion processes of type (X-epsilon(t), Y-epsilon(t)) with null-recurrent fast component X-epsilon(t). In contrast with positive recurrent setting, the slow component Y-epsilon(t) alone cannot be approximated by diffusion processes. However, one can approximate the pair (X-epsilon(t), Y-epsilon(t)) by a Markov diffusion with coefficients averaged in some sense. (C) 2001 Elsevier Science B.V. All rights reserved.