User:JaMs8899/sandbox

In probability theory, branching Brownian motion is a stochastic process which models systems in continuous time which have both random motion in space (modelled by Brownian motion) and branching. It is an example of a branching process, and can be see as the continuous version of the branching random walk.

Branching Brownian motion was first proposed by Ikeda, Nagasawa and Watanabe as an example of a branching diffusion process. It has since been much studied in the literature. It is of interest because of it's connection with the Fisher-KPP equation.

Variants of Branching Brownian Motion

 * Kesten proposed a variant of branching Brownian motion on the real line in which when a particle hits the origin it is killed.


 * Brunet and Derrida proposed a variant in which we keep a constant population of size N by killing some particles of the lowest fitness at each branching event.