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

Abstract

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.