Limiting Distribution of Particles Near the Frontier in the Catalytic Branching Brownian Motion

Sergey Bocharov

doi:10.1007/s10440-019-00305-w

Limiting Distribution of Particles Near the Frontier in the Catalytic Branching Brownian Motion

Sergey Bocharov^*

^*Corresponding author for this work

Zhejiang University

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

7 Citations (Scopus)

Abstract

We consider the model of branching Brownian motion with a single catalytic point at the origin and binary branching. We establish some fine results for the asymptotic behaviour of the numbers of particles travelling at different speeds and in particular prove that the point process of particles travelling at the critical speed converges in distribution to a mixture of Poisson point processes.

Original language	English
Pages (from-to)	433-453
Number of pages	21
Journal	Acta Applicandae Mathematicae
Volume	169
Issue number	1
DOIs	https://doi.org/10.1007/s10440-019-00305-w
Publication status	Published - 1 Oct 2020
Externally published	Yes

Keywords

Branching Brownian motion
Catalytic branching

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title = "Limiting Distribution of Particles Near the Frontier in the Catalytic Branching Brownian Motion",

abstract = "We consider the model of branching Brownian motion with a single catalytic point at the origin and binary branching. We establish some fine results for the asymptotic behaviour of the numbers of particles travelling at different speeds and in particular prove that the point process of particles travelling at the critical speed converges in distribution to a mixture of Poisson point processes.",

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AB - We consider the model of branching Brownian motion with a single catalytic point at the origin and binary branching. We establish some fine results for the asymptotic behaviour of the numbers of particles travelling at different speeds and in particular prove that the point process of particles travelling at the critical speed converges in distribution to a mixture of Poisson point processes.

KW - Branching Brownian motion

KW - Catalytic branching

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JO - Acta Applicandae Mathematicae

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Limiting Distribution of Particles Near the Frontier in the Catalytic Branching Brownian Motion

Abstract

Keywords

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