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Media type:
E-Article
Title:
A Conditional Limit Theorem for the Frontier of a Branching Brownian Motion
Contributor:
Lalley, S. P.;
Sellke, T.
Published:
Institute of Mathematical Statistics, 1987
Published in:
The Annals of Probability, 15 (1987) 3, Seite 1052-1061
Language:
English
ISSN:
0091-1798
Origination:
Footnote:
Description:
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.