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1 results

  • The growth and composition of branching populations

  • Peter Jagers, Olle Nerman
  • Journal:
    Advances in Applied Probability / Volume 16 / Issue 2 / June 1984
    Published online by Cambridge University Press:
    01 July 2016, pp. 221-259
    Print publication:
    June 1984

  • 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.