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On a property of finite-state birth and death processes

Published online by Cambridge University Press:  24 August 2016

A. J. Branford
A. J. Branford*
Affiliation:
The Flinders University of South Australia
*
∗Postal address: School of Mathematical Sciences, The Flinders University of South Australia, Bedford Park, SA 5042, Australia.
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Abstract

A simple proof is given of the result that the ‘overflow' from a finite-state birth and death process is a renewal stream characterized by hyperexponential inter-event times. Our structure is utilized to give a converse result that any hyperexponential renewal stream can be so produced as the overflow from a finite-state birth and death process.

Keywords

HYPEREXPONENTIALOVERFLOWORTHOGONAL POLYNOMIALS
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 4 , December 1986 , pp. 859 - 866
Copyright
Copyright © Applied Probability Trust 1986 

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