Branching Brownian Motion with Catalytic Branching at the Origin

Sergey Bocharov; Simon C. Harris

doi:10.1007/s10440-014-9879-y

Branching Brownian Motion with Catalytic Branching at the Origin

Sergey Bocharov, Simon C. Harris^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

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 language	English
Pages (from-to)	201-228
Number of pages	28
Journal	Acta Applicandae Mathematicae
Volume	134
Issue number	1
DOIs	https://doi.org/10.1007/s10440-014-9879-y
Publication status	Published - 1 Nov 2014
Externally published	Yes

Keywords

Brownian motion
Catalytic branching

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10.1007/s10440-014-9879-y

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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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AB - 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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KW - Catalytic branching

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Branching Brownian Motion with Catalytic Branching at the Origin

Abstract

Keywords

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