WIAS Preprint No. 1062, (2005)

The critical Galton--Watson process without further power moments



Authors

  • Nagaev, Sergei
  • Wachtel, Vitali

2010 Mathematics Subject Classification

  • 60J80 60F05

Keywords

  • critical Galton-Watson process, conditional limit theorem, slowly varying function, functional normalization

Abstract

In this paper we prove a conditional limit theorem for a critical Galton-Watson branching process 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 give also an alternative proof of Sze's (1976) result on the asymptotic behavior of the nonextinction probability.

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