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1 results

  • The Critical Galton-Watson Process Without Further Power Moments

  • Part of
  • S. V. Nagaev, V. Wachtel
  • Journal:
    Journal of Applied Probability / Volume 44 / Issue 3 / September 2007
    Published online by Cambridge University Press:
    14 July 2016, pp. 753-769
    Print publication:
    September 2007
    • Article
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  • In this paper we prove a conditional limit theorem for a critical Galton-Watson branching process {Zn; n ≥ 0} with offspring generating function s + (1 − s)L((1 − s)−1), where L(x) is slowly varying. In contrast to a well-known theorem of Slack (1968), (1972) we use a functional normalization, which gives an exponential limit. We also give an alternative proof of Sze's (1976) result on the asymptotic behavior of the nonextinction probability.