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July, 1988 Traveling Waves in Inhomogeneous Branching Brownian Motions. I
S. Lalley, T. Sellke
Ann. Probab. 16(3): 1051-1062 (July, 1988). DOI: 10.1214/aop/1176991677


Consider a branching Brownian motion for which the instantaneous branching rate of a particle at position $x$ is given by $\beta(x)$. We assume that $\beta$ is an integrable continuous function converging to 0 as $x \rightarrow \pm \infty$. Let $R(t)$ be the position of the rightmost descendant at the time $t$ of a simple particle starting from position 0 at time 0. We show that there exists a constant $\lambda_0 > 0$ such that $R(t) - \sqrt{\lambda_0/2} t$ converges in distribution as $t \rightarrow \infty$ to a location mixture of the extreme value distribution $\exp (e^{-\sqrt{2\lambda_0 x}})$.


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S. Lalley. T. Sellke. "Traveling Waves in Inhomogeneous Branching Brownian Motions. I." Ann. Probab. 16 (3) 1051 - 1062, July, 1988.


Published: July, 1988
First available in Project Euclid: 19 April 2007

zbMATH: 0658.60113
MathSciNet: MR942755
Digital Object Identifier: 10.1214/aop/1176991677

Primary: 60J80
Secondary: 60F05 , 60G55

Keywords: extreme value distribution , Inhomogeneous branching Brownian motion , Traveling wave

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 3 • July, 1988
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