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Asymptotic results for the extinction time of Markov branching processes allowing emigration, I. Random walk decrements

Published online by Cambridge University Press:  01 July 2016

Anthony G. Pakes
Anthony G. Pakes*
Affiliation:
University of Western Australia
*
∗Postal address: Department of Mathematics, University of Western Australia, Nedlands, WA 6009, Australia.
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Abstract

The mathematical model is a Markov branching process which is subjected to catastrophes or large-scale emigration. Catastrophes reduce the population size by independent and identically distributed decrements, and two mechanisms for generating catastrophe epochs are given separate consideration. These are that catastrophes occur at a rate proportional to population size, and as an independent Poisson process.

The paper studies some properties of the time to extinction of the modified process in those cases where extinction occurs almost surely. Particular attention is given to limit theorems and the behaviour of the expected extinction time as the initial population size grows. These properties are contrasted with known properties for the case when there is no catastrophe component.

Keywords

LINEAR BIRTH AND DEATH PROCESSCATASTROPHES AND EMIGRATIONLIMIT THEOREMS
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 2 , June 1989 , pp. 243 - 269
Copyright
Copyright © Applied Probability Trust 1989 

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Footnotes

This research was partially supported by N.S.F. Grant DMS-8501763 during a visit to Colorado State University.

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