Branching Brownian Motion with catalytic branching at the origin

Sergey Bocharov; Simon C. Harris

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arXiv · 1302.4087

Branching Brownian Motion with catalytic branching at the origin

Sergey Bocharov·Simon C. Harris

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Abstract

We consider a branching Brownian motion in which binary fission takes place only when particles are at the origin at a rate \beta > 0 on the local time scale. We obtain results regarding the asymptotic behaviour of the number of particles above \lambda t at time t, for \lambda > 0. As a corollary, we establish the almost sure asymptotic speed of the rightmost particle. We also prove a Strong Law of Large Numbers for this catalytic branching Brownian motion.

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Sergey Bocharov, Simon C. Harris. 2013-02-17. Branching Brownian Motion with catalytic branching at the origin. https://arxiv.org/abs/1302.4087

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