Translator Disclaimer
September 2013 On largest offspring in a critical branching process with finite variance
Jean Bertoin
Author Affiliations +
J. Appl. Probab. 50(3): 791-800 (September 2013). DOI: 10.1239/jap/1378401236

Abstract

Continuing the work in Bertoin (2011) we study the distribution of the maximal number X*k of offspring amongst all individuals in a critical Galton‒Watson process started with k ancestors, treating the case when the reproduction law has a regularly varying tail with index −α for α>2 (and, hence, finite variance). We show that X*k suitably normalized converges in distribution to a Fréchet law with shape parameter α/2; this contrasts sharply with the case 1< α<2 when the variance is infinite. More generally, we obtain a weak limit theorem for the offspring sequence ranked in decreasing order, in terms of atoms of a certain doubly stochastic Poisson measure.

Citation

Download Citation

Jean Bertoin. "On largest offspring in a critical branching process with finite variance." J. Appl. Probab. 50 (3) 791 - 800, September 2013. https://doi.org/10.1239/jap/1378401236

Information

Published: September 2013
First available in Project Euclid: 5 September 2013

zbMATH: 1277.60045
MathSciNet: MR3188595
Digital Object Identifier: 10.1239/jap/1378401236

Subjects:
Primary: 60F05, 60J80

Rights: Copyright © 2013 Applied Probability Trust

JOURNAL ARTICLE
10 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.50 • No. 3 • September 2013
Back to Top