A conditional limit theorem for the frontier of a branching Brownian motion
type: Item
instance of: scholarly article
title: A conditional limit theorem for the frontier of a branching Brownian motion
zbMATH Open document ID: 0622.60085
published in: The Annals of Probability
publication date: 1987-01-01T00:00:00Z
review text: We prove a weak limit theorem which relates the large time behavior of the maximum of a branching Brownian motion to the limiting value of a certain associated martingale. This exhibits the minimal velocity travelling wave for the KPP-Fisher equation as a translation mixture of extreme-value distributions. We also show that every particle in a branching Brownian motion has a descendant at the frontier at some time. A final section states several conjectures concerning a hypothesized stationary ''standing wave of particles'' process and the relationship of this process to branching Brownian motion.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 4009482
zbMATH Keywords: weak limit theorem
zbMATH Keywords: large time behavior
zbMATH Keywords: mixture of extreme-value distributions
zbMATH Keywords: branching Brownian motion
author: Steven P. Lalley
author: Thomas M. Sellke
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992080
OpenAlex ID: W2006851042
DOI: 10.1214/AOP/1176992080
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description: scientific article; zbMATH DE number 4009482