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The extinction time of a general birth and death process with catastrophes

Published online by Cambridge University Press:  24 August 2016

P. J. Brockwell
P. J. Brockwell*
Affiliation:
Colorado State University
*
∗Postal address: Department of Statistics, Colorado State University, Fort Collins, CO 80523, USA.
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Abstract

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfy λ0 = 0, λ j > 0 for each j > 0, and . Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λ j = jλ, µj = jμ) with catastrophes of several different types.

Keywords

MARKOVIAN POPULATION MODELEXTINCTION TIME
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 4 , December 1986 , pp. 851 - 858
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

Research supported by NSF Grant No. DMS 85 01912

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