Supercritical Branching Brownian Motion and K‐P‐P Equation In the Critical Speed‐Area
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<jats:title>Abstract</jats:title><jats:p>If <jats:italic>R</jats:italic><jats:sub>t</jats:sub> is the position of the rightmost particle at time <jats:italic>t</jats:italic> in a one dimensional branching brownian motion, <jats:disp-formula> </jats:disp-formula> whore α is the inverse of the mean life time and <jats:italic>m</jats:italic> is the mean of the reproduction law. If <jats:italic>Z</jats:italic><jats:sub>t</jats:sub> denotes the random point measure of particles living at time <jats:italic>t</jats:italic>, we get in the critical area {c = c<jats:sub>0</jats:sub>} <jats:disp-formula> </jats:disp-formula> The function u(t, x) = P(R<jats:sub>t</jats:sub> > x) is studied as a solution of the K‐P‐P equation <jats:disp-formula> </jats:disp-formula> for some function <jats:italic>f.</jats:italic></jats:p><jats:p>Conditioned on non‐extinction of the spatial tree in the <jats:italic>c</jats:italic><jats:sub>0</jats:sub>‐direction, a limit distribution is obtained and characterized.</jats:p>
収録刊行物
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- Mathematische Nachrichten
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Mathematische Nachrichten 149 (1), 41-59, 1990-01
Wiley