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Supercritical age-dependent branching processes with immigration

Published online by Cambridge University Press:  14 July 2016

K. B. Athreya ,
P. R. Parthasarathy  and
G. Sankaranarayanan
K. B. Athreya
Affiliation:
Indian Institute of Science, Bangalore
P. R. Parthasarathy
Affiliation:
Annamalai University, Annamalai Nagar
G. Sankaranarayanan
Affiliation:
Annamalai University, Annamalai Nagar
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Abstract

A branching process with immigration of the following type is considered. For every i, a random number Ni of particles join the system at time . These particles evolve according to a one-dimensional age-dependent branching process with offspring p.g.f. and life time distribution G(t). Assume . Then it is shown that Z(t) e–αt converges in distribution to an extended real-valued random variable Y where a is the Malthusian parameter. We do not require the sequences {τi} or {Ni} to be independent or identically distributed or even mutually independent.

Keywords

SUPERCRITICALIMMIGRATIONAGE-DEPENDENTBRANCHING PROCESSESMALTHUSIAN PARAMETERCONVERGENCE IN DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 4 , December 1974 , pp. 695 - 702
Copyright
Copyright © Applied Probability Trust 1974 

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References

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