The Critical Galton-Watson Process Without Further Power Moments

Abstract

In this paper we prove a conditional limit theorem for a critical Galton-Watson branching process { Z n ; 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.

Identifiers

DOI

10.1239/jap/1189717543

Citations and references