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Birth, immigration and catastrophe processes

Published online by Cambridge University Press:  01 July 2016

P. J. Brockwell,
J. Gani and
S. I. Resnick
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.
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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.

Keywords

POPULATION PROCESSESBIRTH, DEATH, IMMIGRATION AND CATASTROPHE PROCESSESMARKOV MODELSSEMISTOCHASTIC MODELSTIME TO EXTINCTION

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 4 , December 1982, pp. 709 - 731
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.

References

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