The Critical Galton-Watson Process Without Further Power Moments

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, whi...

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Veröffentlicht in:	Journal of applied probability 2007-09, Vol.44 (3), p.753-769
Hauptverfasser:	Nagaev, S. V., Wachtel, V.
Format:	Artikel
Sprache:	eng
Schlagworte:	60F05 60J80 Asymptotic methods conditional theorem Critical Galton-Watson process Distribution functions Generating function Logarithms Mathematical functions Mathematical theorems Probability Random variables slowly varying function Stochastic models Studies
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