Branching Brownian Motion with catalytic branching at the origin
Abstract
We consider a branching Brownian motion in which binary fission takes place only when particles are at the origin at a rate β > 0 on the local time scale. We obtain results regarding the asymptotic behaviour of the number of particles above λ t at time t, for λ > 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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