If Rt 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 Zt denotes the random point measure of particles living at time t, we get in the critical area {c = c0} The function u(t, x) = P(Rt > 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 c0‐direction, a limit distribution is obtained and characterized.
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Chauvin et al. (1990) studied this question.
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