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

Published online by Cambridge University Press:  14 July 2016

J. Keilson
J. Keilson*
Affiliation:
The University of Birmingham, Sylvania Electronic Systems, Waltham, Massachusetts
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Extract

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.

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Type
Research Papers
Information
Journal of Applied Probability , Volume 1 , Issue 2 , December 1964 , pp. 247 - 266
Copyright
Copyright © Applied Probability Trust 

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