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On supercritical Galton-Watson processes allowing immigration

Published online by Cambridge University Press:  14 July 2016

A. G. Pakes
A. G. Pakes*
Affiliation:
Monash University
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Abstract

We establish the absolute continuity of the limit random variables of two supercritical Galton-Watson branching processes, one allowing unrestricted immigration and the other having a state dependent immigration component.

Keywords

BRANCHING PROCESSESSUPERCRITICALIMMIGRATIONABSOLUTE CONTINUITY
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 4 , December 1974 , pp. 814 - 817
Copyright
Copyright © Applied Probability Trust 1974 

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References

Athreya, K. B. (1969) On the supercritical one dimensional age dependent branching process. Ann. Math. Statist. 40, 743–763.Google Scholar
Athreya, K. B. (1971) On the absolute continuity of the limit random variable in the supercritical Galton-Watson branching process. Proc. Amer. Math. Soc. 30, 563–565.Google Scholar
Athreya, K. B. and Ney, P. E. (1972) Branching Processes. Springer, Berlin.Google Scholar
Pakes, A. G. (1971a) Branching processes with immigration. J. Appl. Prob. 8, 32–42.Google Scholar
Pakes, A. G. (1971b) A branching process with a state dependent immigration component. Adv. Appl. Prob. 3, 301–314.Google Scholar
Seneta, E. (1970) On the supercritical Galton-Watson process with immigration. Math. Biosci. 7, 9–14.Google Scholar