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A branching process with disasters

Published online by Cambridge University Press:  14 July 2016

Norman Kaplan ,
Aidan Sudbury  and
Trygve S. Nilsen
Norman Kaplan
Affiliation:
University of California, Berkeley
Aidan Sudbury
Affiliation:
University of California, Berkeley
Trygve S. Nilsen
Affiliation:
University of Bergen, Norway
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Abstract

A population process is considered where particles reproduce according to an age-dependent branching process, and are subjected to disasters which occur at the epochs of an independent renewal process. Each particle alive at the time of a disaster, survives it with probability p and the survival of any particle is assumed independent of the survival of any other particle. The asymptotic behavior of the mean of the process is determined and as a consequence, necessary and sufficient conditions are given for extinction.

Keywords

BRANCHING MODELGENERALIZED BRANCHING PROCESSRENEWAL THEORY
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 1 , March 1975 , pp. 47 - 59
Copyright
Copyright © Applied Probability Trust 1975 

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References

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[8] Athreya, K. B. and Kaplan, N. (1974) Limit theorems for a branching process with disastes. To appear.Google Scholar