Degenerative convergence of diffusion process toward a submanifold by strong drift

Abstract

Letbe a diffusion process on a Riemannian manifold Nhaving an infinitesimal generator. We investigate the asymptotic behavior of as the strength β of the drift becomes large under the situation that the set Mof asymptotically stable fixed points of the vector field bforms a submanifold of N. It is shown that converges to a diffusion process on Mas β tends to infinity and the generator of the limit diffusion is specified based on the perturbation method.