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1 results

  • The age of a Galton-Watson population with a geometric offspring distribution

  • Part of
  • F. C. Klebaner, S. Sagitov
  • Journal:
    Journal of Applied Probability / Volume 39 / Issue 4 / December 2002
    Published online by Cambridge University Press:
    14 July 2016, pp. 816-828
    Print publication:
    December 2002

  • Motivated by the question of the age in a branching population we try to recreate the past by looking back from the currently observed population size. We define a new backward Galton-Watson process and study the case of the geometric offspring distribution with parameter p in detail. The backward process is then the Galton-Watson process with immigration, again with a geometric offspring distribution but with parameter 1-p, and it is also the dual to the original Galton-Watson process. We give the asymptotic distribution of the age when the initial population size is large in supercritical and critical cases. To this end, we give new asymptotic results on the Galton-Watson immigration processes stopped at zero.