A review of transient behavior in regular diffusion and birth-death processes
- 1 December 1964
- journal article
- review article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 1 (2) , 247-266
- https://doi.org/10.1017/s0021900200108381
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.Keywords
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