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The extinction time of a birth, death and catastrophe process and of a related diffusion model

Published online by Cambridge University Press:  01 July 2016

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

The distribution of the extinction time for a linear birth and death process subject to catastrophes is determined. The catastrophes occur at a rate proportional to the population size and their magnitudes are random variables having an arbitrary distribution with generating function d(·). The asymptotic behaviour (for large initial population size) of the expected time to extinction is found under the assumption that d(.) has radius of convergence greater than 1. Corresponding results are derived for a related class of diffusion processes interrupted by catastrophes with sizes having an arbitrary distribution function.

Keywords

MARKOVIAN POPULATION PROCESSTIME TO EXTINCTIONDIFFUSION PROCESS WITH DOWNWARD JUMPS
Type
Research Article
Information
Advances in Applied Probability , Volume 17 , Issue 1 , March 1985 , pp. 42 - 52
Copyright
Copyright © Applied Probability Trust 1985 

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Footnotes

Research carried out while on leave from Colorado State University and partially supported by NSF Grant No. MCS 82 02335.

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