Feller property of skew product diffusion processes

Abstract

Feller property of some diffusion processes and the time changed processes is investigated. Diffusion processes treated here are skew product of one dimensional generalized diffusion processes and the spherical Brownian motion, and the time changed processes are given by additive functional associated with some underlying measure. Concrete expressions of the Dirichlet forms corresponding to time changed processes are also obtained, which may be of non-local type caused by degeneracy of the underlying measures.