WIAS Preprint No. 1062, (2005)
The critical Galton--Watson process without further power moments
- Nagaev, Sergei
- Wachtel, Vitali
2010 Mathematics Subject Classification
- 60J80 60F05
- critical Galton-Watson process, conditional limit theorem, slowly varying function, functional normalization
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.