On the maximum sequence in a critical branching process
type: Item
instance of: scholarly article
title: On the maximum sequence in a critical branching process
zbMATH Open document ID: 0643.60063
published in: The Annals of Probability
publication date: 1988-01-01T00:00:00Z
review text: Let \(\{Z_ n\}\) be a critical branching process in which the family size has finite variance. Let \(M_ n\) be the maximum population size up to the n th generation, so \(M_ n=\max \{Z_ j:0\leq j\leq n\}\). It is a consequence of results of \textit{A. G. Pakes} [J. Appl. Probab. 24, 768-772 (1987; Zbl 0636.60047)] that, if \(Z_ 0=i\), lim sup(E(M\({}_ n)/\log n)\leq i\). Here it is shown that, if \(Z_ 0=i\), \(E(M_ n)/\log n\to i\) as \(n\to \infty\).
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60K99
zbMATH DE Number: 4048800
zbMATH Keywords: critical branching process
zbMATH Keywords: maximum population size
author: K. B. Athreya
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176991770
OpenAlex ID: W2093970942
DOI: 10.1214/AOP/1176991770
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description: scientific article; zbMATH DE number 4048800