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Birth, immigration and catastrophe processes

Published online by Cambridge University Press:  01 July 2016

P. J. Brockwell*
Affiliation:
Colorado State University
J. Gani*
Affiliation:
University of Kentucky
S. I. Resnick*
Affiliation:
Colorado State University
*
Postal address: Department of Statistics, Colorado State University, Fort Collins, CO 80523, U.S.A.
∗∗Postal address: Department of Statistics, University of Kentucky, Lexington, KY 40506, U.S.A.
Postal address: Department of Statistics, Colorado State University, Fort Collins, CO 80523, U.S.A.

Abstract

We consider Markov models for growth of populations subject to catastrophes. Emphasis is placed on discrete-state models where immigration is possible and the catastrophe rate is population-dependent. Explicit formulas for descriptive quantities of interest are derived when catastrophes reduce population size by a random amount which is either geometrically, binomially or uniformly distributed. Comparison is made with continuous-state Markov models in the literature in which population size evolves continuously and deterministically upwards between random jumps downward.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

Research partially supported by NSF Grant No. MCS 78 00915-01.

Portions of this work were done during a visit to the Department of Statistics, Colorado State University, to which grateful acknowledgement is made for hospitality and support.

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