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A note on the subcritical generalized age-dependent branching process

Published online by Cambridge University Press:  14 July 2016

R. A. Doney
R. A. Doney*
Affiliation:
University of Manchester
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Abstract

For a subcritical Bellman-Harris process for which the Malthusian parameter α exists and the mean function M(t)∼ aeat as t → ∞, a necessary and sufficient condition for e–at (1 –F(s, t)) to have a non-zero limit is known. The corresponding condition is given for the generalized branching process.

Keywords

GENERALIZED AGE-DEPENDENT BRANCHING PROCESSSUBCRITICAL BRANCHING PROCESS
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 4 , December 1976 , pp. 798 - 803
Copyright
Copyright © Applied Probability Trust 1976 

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References

[1] Athreya, K. B. and Ney, P. E. (1972) Branching Processes. Springer, Berlin.CrossRefGoogle Scholar
[2] Doney, R. A. (1972) A limit theorem for a class of supercritical branching processes. J. Appl. Prob. 9, 707–724.CrossRefGoogle Scholar
[3] Doney, R. A. (1976) On single- and multi-type general age-dependent branching processes. J. Appl. Prob. 13, 239–246.CrossRefGoogle Scholar
[4] Ryan, T. A. (1968) On Age-dependent Branching Processes. , Cornell University.Google Scholar