A review of transient behavior in regular diffusion and birth-death processes

Abstract

Our concern is with passage times and rate of approach to ergodicity for two types of temporally homogeneous processes, doubly bounded diffusion processes in one dimension, and birth-death processes on the finite lattice. The passage time problems associated with these processes are of considerable practical interest, but for many important cases, e.g., the Uhlenbeck-Ornstein process, only formal solutions such as Laplace transforms (cf. Darling and Siegert, 1953) have been given, with limited numerical potential.