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

Published online by Cambridge University Press:  14 July 2016

J. Keilson
J. Keilson*
Affiliation:
Sylvania Electronic Systems, Waltham, Massachussetts
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Extract

A previous paper, hereafter referred to as “I”, reviewed the structure of a class of “regular” diffusion and birth-death processes in one dimension. Such processes were seen to have a basic simplicity manifesting itself in two ways: (1) The ergodic processes have an ergodic distribution that one may write down at once; (2) All such processes have transition functions for which a simple spectral representation is available. The simple spectral structure affords theoretical insight into the structure of related passage time densities, and numerical techniques for their evaluation. In particular, a variational principle is available for estimating the principal eigenvalues and eigenvectors.

Type
Research Papers
Information
Journal of Applied Probability , Volume 2 , Issue 2 , December 1965 , pp. 405 - 428
Copyright
Copyright © Applied Probability Trust 

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