Acta Applicandae Mathematicae

, Volume 134, Issue 1, pp 201–228

Branching Brownian Motion with Catalytic Branching at the Origin

Article

DOI: 10.1007/s10440-014-9879-y

Cite this article as:
Bocharov, S. & Harris, S.C. Acta Appl Math (2014) 134: 201. doi:10.1007/s10440-014-9879-y

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.

Keywords

Catalytic branching Brownian motion 

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang UniversityHangzhouChina
  2. 2.Department of Mathematical SciencesUniversity of BathBathUK

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