Branching Brownian Motion with Catalytic Branching at the Origin

作者:Bocharov, Sergey; Harris, Simon C.*
来源:Acta Applicandae Mathematicae, 2014, 134(1): 201-228.
DOI:10.1007/s10440-014-9879-y

摘要

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.