Open Access
July, 1987 A Conditional Limit Theorem for the Frontier of a Branching Brownian Motion
S. P. Lalley, T. Sellke
Ann. Probab. 15(3): 1052-1061 (July, 1987). DOI: 10.1214/aop/1176992080


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.


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S. P. Lalley. T. Sellke. "A Conditional Limit Theorem for the Frontier of a Branching Brownian Motion." Ann. Probab. 15 (3) 1052 - 1061, July, 1987.


Published: July, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0622.60085
MathSciNet: MR893913
Digital Object Identifier: 10.1214/aop/1176992080

Primary: 60J60

Keywords: Branching Brownian motion , extreme-value distribution , KPP-Fisher equation , Travelling wave

Rights: Copyright © 1987 Institute of Mathematical Statistics

Vol.15 • No. 3 • July, 1987
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