A Conditional Limit Theorem for the Frontier of a Branching Brownian Motion
Lalley, S. P. ; Sellke, T.
Ann. Probab., Tome 15 (1987) no. 4, p. 1052-1061 / Harvested from Project Euclid
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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.
Publié le : 1987-07-14
Classification:  Branching Brownian motion,  KPP-Fisher equation,  travelling wave,  extreme-value distribution,  60J60 
@article{1176992080,
     author = {Lalley, S. P. and Sellke, T.},
     title = {A Conditional Limit Theorem for the Frontier of a Branching Brownian Motion},
     journal = {Ann. Probab.},
     volume = {15},
     number = {4},
     year = {1987},
     pages = { 1052-1061},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176992080}
}

Lalley, S. P.; Sellke, T. A Conditional Limit Theorem for the Frontier of a Branching Brownian Motion. Ann. Probab., Tome 15 (1987) no. 4, pp.  1052-1061. http://gdmltest.u-ga.fr/item/1176992080/