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June 2011 On the maximal offspring in a critical branching process with infinite variance
Jean Bertoin
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J. Appl. Probab. 48(2): 576-582 (June 2011). DOI: 10.1239/jap/1308662646

Abstract

We investigate the maximal number Mk of offspringamongst all individuals in a critical Galton-Watson process started withk ancestors. We show that when the reproduction law has a regularlyvarying tail with index -α for 1 < α < 2, thenk-1Mk converges in distribution to aFrechet law with shape parameter 1 and scale parameter depending only onα.

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Jean Bertoin. "On the maximal offspring in a critical branching process with infinite variance." J. Appl. Probab. 48 (2) 576 - 582, June 2011. https://doi.org/10.1239/jap/1308662646

Information

Published: June 2011
First available in Project Euclid: 21 June 2011

zbMATH: 1223.60020
MathSciNet: MR2840318
Digital Object Identifier: 10.1239/jap/1308662646

Subjects:
Primary: 60F05, 60J80

Rights: Copyright © 2011 Applied Probability Trust

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Vol.48 • No. 2 • June 2011
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