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Exponential growth of a branching process usually implies stable age distribution

Published online by Cambridge University Press:  14 July 2016

Bo Berndtsson  and
Peter Jagers
Bo Berndtsson*
Affiliation:
Chalmers University of Technology and University of Göteborg
Peter Jagers*
Affiliation:
Chalmers University of Technology and University of Göteborg
*
∗ Postal address: Department of Mathematics, Chalmers University of Technology and University of Göteborg, Fack, S–412 96 Göteborg, Sweden.
∗ Postal address: Department of Mathematics, Chalmers University of Technology and University of Göteborg, Fack, S–412 96 Göteborg, Sweden.
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Abstract

Start a Bellman–Harris branching process from one or several ancestors, whose ages are identically distributed random variables. Assume that the life-length distribution decays more quickly than exponentially and that the distribution of ages at start does not give too much mass to high ages (in a sense to be made precise). Then, if the expected population size is an exponential function of time, the ages must follow the stable age distribution of the process.

Keywords

BRANCHING PROCESSSTABLE AGE DISTRIBUTIONCONVOLUTIONBOUNDED ANALYTIC FUNCTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 16 , Issue 3 , September 1979 , pp. 651 - 656
Copyright
Copyright © Applied Probability Trust 1979 

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References

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