Branching Brownian Motion with Catalytic Branching at the Origin |
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Authors: | Sergey Bocharov Simon C Harris |
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Institution: | 1. Department of Mathematics, Zhejiang University, Zheda Road, Hangzhou, 310027, China 2. Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, UK
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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 β>0 on the local time scale. We obtain results regarding the asymptotic behaviour of the number of particles above λt 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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