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The simple branching process with infinite mean. I

Published online by Cambridge University Press:  14 July 2016

E. Seneta
E. Seneta*
Affiliation:
Australian National University, Canberra
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Abstract

The simple branching process {Zn} with mean number of offspring per individual infinite, is considered. Conditions under which there exists a sequence {pn} of positive constants such that pn log (1 +Zn) converges in law to a proper limit distribution are given, as is a supplementary condition necessary and sufficient for pn~ constant cn as n→∞, where 0 < c < 1 is a number characteristic of the process. Some properties of the limiting distribution function are discussed; while others (with additional results) are deferred to a sequel.

Keywords

BRANCHING PROCESSGALTON-WATSON PROCESSINFINITE MEANCONVEXITYFUNCTIONAL ITERATION
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 1 , March 1973 , pp. 206 - 212
Copyright
Copyright © Applied Probability Trust 1973 

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References

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