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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
Norman Kaplan*
Affiliation:
University of California, Berkeley
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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.

Keywords

GENERALIZED AGE-DEPENDENT BRANCHING PROCESSSUPERCRITICAL BRANCHING PROCESS
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 2 , June 1975 , pp. 341 - 345
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, 743–763.Google Scholar
[2] Doney, R. A. (1972) A limit theorem for a class of supercritical branching process. J. Appl. Prob. 9, 707–725.Google Scholar