The Annals of Probability
- Ann. Probab.
- Volume 15, Number 3 (1987), 1052-1061.
A Conditional Limit Theorem for the Frontier of a Branching Brownian Motion
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.
Ann. Probab., Volume 15, Number 3 (1987), 1052-1061.
First available in Project Euclid: 19 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J60: Diffusion processes [See also 58J65]
Lalley, S. P.; Sellke, T. A Conditional Limit Theorem for the Frontier of a Branching Brownian Motion. Ann. Probab. 15 (1987), no. 3, 1052--1061. doi:10.1214/aop/1176992080. https://projecteuclid.org/euclid.aop/1176992080