Branching Brownian Motion with catalytic branching at the origin

2013/02/17 by Sergey Bocharov, Simon C. Harris, Bocharov, Sergey +1 · 2 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1302.4087

openalex publication_date 2013/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Extremes of Brownian Decision Trees
• Geometric control of boundary-catalytic branching processes

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