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The stable pedigrees of critical branching populations

Published online by Cambridge University Press:  14 July 2016

Olle Nerman
Olle Nerman*
Affiliation:
University of Göteborg
*
∗Postal address: Mathematical Statistics, Department of Mathematics, Chalmers University of Technology and the University of Göteborg, S-412 96 Göteborg, Sweden
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Abstract

The asymptotic sizes and compositions of critical general branching processes conditioned on non-extinction are treated. First, results are given for processes counted with random characteristics allowed to depend on the whole daughter processes, then these are used to derive conditional limit theorems for the pedigrees of randomly sampled individuals among populations counted with 0–1-valued characteristics. The limiting stable pedigrees have nice independence structures and are easily derived from the original branching laws.

Keywords

BRANCHING PROCESSPOPULATION DYNAMICSSTABLE AGE DISTRIBUTIONCELL KINETICS
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 3 , September 1984 , pp. 447 - 463
Copyright
Copyright © Applied Probability Trust 1984 

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Footnotes

This work has been supported by a grant from the Swedish Natural Science Research Council.

References

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