The growth and spread of the general branching random walk
type: Item
instance of: scholarly article
title: The growth and spread of the general branching random walk
zbMATH Open document ID: 0859.60075
author: J. D. Biggins
published in: The Annals of Applied Probability
publication date: 1997-04-09T00:00:00Z
review text: This is a companion paper to [the author, in: Classical and modern branching processes (ed. Athreya and Jagers, Springer, New York (1996)]. A general (Crump-Mode-Jagers) spatial branching process is considered. The asymptotic behavior of the numbers present at time \(t\) in sets of the form \([ta,\infty)\) is obtained. As a consequence it is shown that if \(B_t\) is the position of the rightmost person at time \(t\), \(B_t/t\) converges to a constant, which can be obtained from the individual reproduction law, almost surely on the survival set of the process. This generalizes the known discrete-time results.
reviewed by: M. P. Quine
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 898167
zbMATH Keywords: spatial spread
zbMATH Keywords: Crump-Mode-Jagers branching process
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1177004604
OpenAlex ID: W2049189093
DOI: 10.1214/AOAP/1177004604
description: scientific article; zbMATH DE number 898167