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On higher moments of the population size in a subcritical branching process

Published online by Cambridge University Press:  14 July 2016

Eric Willekens
Eric Willekens*
Affiliation:
Catholic University Leuven
*
∗Present address: Department of Mathematics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.
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Abstract

Let {Z(t), t ≧ 0} be an age-dependent subcritical branching process. In this paper we show that if the lifetime distribution is subexponential, EZα (t) ~ EZ(t) (t →∞) for every α ≧ 1. If furthermore the lifetime distribution has a subexponential density, a rate of convergence result in the above relation is established.

Keywords

SUBEXPONENTIAL DISTRIBUTIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 25 , Issue 2 , June 1988 , pp. 413 - 417
Copyright
Copyright © Applied Probability Trust 1988 

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Footnotes

The author is a research assistant of the Belgian National Fund for Scientific Research.

References

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