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The growth and composition of branching populations

Published online by Cambridge University Press:  01 July 2016

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

A single-type general branching population develops by individuals reproducing according to i.i.d. point processes on R+, interpreted as the individuals' ages. Such a population can be measured or counted in many different ways: those born, those alive or in some sub-phase of life, for example. Special choices of reproduction point process and counting yield the classical Galton–Watson or Bellman–Harris process. This reasonably self-contained survey paper discusses the exponential growth of such populations, in the supercritical case, and the asymptotic stability of composition according to very general ways of counting. The outcome is a strict definition of a stable population in exponential growth, as a probability space, a margin of which is the well-known stable age distribution.

Keywords

BRANCHING PROCESSSTABLE POPULATION THEORYBALANCED EXPONENTIAL GROWTH
Type
Research Article
Information
Advances in Applied Probability , Volume 16 , Issue 2 , June 1984 , pp. 221 - 259
Copyright
Copyright © Applied Probability Trust 1984 

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