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Some limit theorems for a supercritical branching process allowing immigration

Published online by Cambridge University Press:  14 July 2016

A. G. Pakes
A. G. Pakes*
Affiliation:
Monash University, Clayton, Victoria
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Abstract

We consider the Bienaymé–Galton–Watson model of population growth in which immigration is allowed. When the mean number of offspring per individual, α, satisfies 1 < α < ∞, a well-known result proves that a normalised version of the size of the n th generation converges to a finite, positive random variable iff a certain condition is satisfied by the immigration distribution. In this paper we obtain some non-linear limit theorems when this condition is not satisfied. Results are also given for the explosive case, α = ∞.

Keywords

BRANCHING PROCESSIMMIGRATIONSUPERCRITICALEXPLOSIVENON-LINEAR LIMIT THEOREMSREGULAR VARIATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 1 , March 1976 , pp. 17 - 26
Copyright
Copyright © Applied Probability Trust 1976 

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References

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