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.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Reference21 articles.
1. Branching Processes
2. Lois empiriques dans les processus de branchement spatiaux homogénes supercritiques;Rouault;C.R. Acad. Sci. Paris,1981
3. On the convergence of supercritical general (C-M-J) branching processes
4. The distribution of generations and other aspects of the family structure of branching processes;Buhler;Proc. 6th Berkeley Symp. Math. Statist. Prob.,1970
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