Supercritical Branching Brownian Motion and K-P-P Equation In the Critical Speed-Area

✍ Scribed by B. Chauvin; A. Rouault

• Publisher: John Wiley and Sons
• Year: 1990
• Tongue: English
• Weight: 603 KB
• Volume: 149
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19901490104

✦ Synopsis

Abstract

If R~t~ is the position of the rightmost particle at time t in a one dimensional branching brownian motion,
whore α is the inverse of the mean life time and m is the mean of the reproduction law. If Z~t~ denotes the random point measure of particles living at time t, we get in the critical area {c = c~0~}
The function u(t, x) = P(R~t~ > x) is studied as a solution of the K‐P‐P equation
for some function f.

Conditioned on non‐extinction of the spatial tree in the c~0~‐direction, a limit distribution is obtained and characterized.