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The Growth and Composition of Branching Populations

Peter Jagers and Olle Nerman
Advances in Applied Probability
Vol. 16, No. 2 (Jun., 1984), pp. 221-259
DOI: 10.2307/1427068
Stable URL: http://www.jstor.org/stable/1427068
Page Count: 39
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The Growth and Composition of Branching Populations
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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.

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