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Bounds for the extinction probability of a simple branching process

Published online by Cambridge University Press:  14 July 2016

M. P. Quine
M. P. Quine*
Affiliation:
University of Sydney
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Abstract

The extinction probability q of a supercritical simple branching process is well known to be less than unity. Intuitively, it is apparent that when the offspring mean is close to one, so, usually, will q be. This notion is made rigorous, and simple bounds are given for q in terms of the second and third factorial moments, which are applicable when the offspring mean is close to unity. A comparison is made of various upper bounds for q. The note contains some numerical examples.

Keywords

BRANCHING PROCESSGALTON–WATSONEXTINCTION PROBABILITYBOUNDSMOMENTSQUEUEING THEORY
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 1 , March 1976 , pp. 9 - 16
Copyright
Copyright © Applied Probability Trust 1976 

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References

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