Branching Brownian Motion with Catalytic Branching at the Origin

Sergey Bocharov, Simon C. Harris

Research output: Contribution to journalArticle

8 Citations (Scopus)
123 Downloads (Pure)

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.

Original languageEnglish
Pages (from-to)201-228
Number of pages28
JournalActa Applicandae Mathematicae
Volume134
Issue number1
DOIs
Publication statusPublished - Dec 2014

Keywords

  • Brownian motion
  • Catalytic branching

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