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A note on the supercritical generalized age-dependent branching process

Published online by Cambridge University Press:  14 July 2016

Norman Kaplan*
Affiliation:
University of California, Berkeley

Abstract

A sufficient condition is given for a supercritical generalized age-dependent branching process, properly normalized, to converge to zero. This condition is the strongest one possible, for if it does not hold, then it is known that the normalized process does indeed converge to a legitimate random variable.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Athreya, K. (1969) On the supercritical one-dimensional age-dependent branching process. Ann. Math. Statist. 40, 743763.Google Scholar
[2] Doney, R. A. (1972) A limit theorem for a class of supercritical branching process. J. Appl. Prob. 9, 707725.Google Scholar