Limiting distribution of the rightmost particle in catalytic branching Brownian motion

Sergey Bocharov; Simon C. Harris

doi:10.1214/16-ECP22

Limiting distribution of the rightmost particle in catalytic branching Brownian motion

Sergey Bocharov, Simon C. Harris

Zhejiang University

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Abstract

We study the model of binary branching Brownian motion with spatially-inhomogeneous branching rate βδ₀(·), where δ₀(·) is the Dirac delta function and β is some positive constant. We show that the distribution of the rightmost particle centred about β/2 t converges to a mixture of Gumbel distributions according to a martingale limit. Our results form a natural extension to S. Lalley and T. Sellke [10] for the degenerate case of catalytic branching.

Original language	English
Article number	Paper no. 70
Number of pages	12
Journal	Electronic Communications in Probability
Volume	21
DOIs	https://doi.org/10.1214/16-ECP22
Publication status	Published - 4 Oct 2016

Keywords

Brownian motion
Catalytic branching
Local time

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10.1214/16-ECP22Licence: CC BY

Published VersionFinal published version, 247 KBLicence: CC BY

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abstract = "We study the model of binary branching Brownian motion with spatially-inhomogeneous branching rate βδ0(·), where δ0(·) is the Dirac delta function and β is some positive constant. We show that the distribution of the rightmost particle centred about β/2 t converges to a mixture of Gumbel distributions according to a martingale limit. Our results form a natural extension to S. Lalley and T. Sellke [10] for the degenerate case of catalytic branching.",

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AU - Harris, Simon C.

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N2 - We study the model of binary branching Brownian motion with spatially-inhomogeneous branching rate βδ0(·), where δ0(·) is the Dirac delta function and β is some positive constant. We show that the distribution of the rightmost particle centred about β/2 t converges to a mixture of Gumbel distributions according to a martingale limit. Our results form a natural extension to S. Lalley and T. Sellke [10] for the degenerate case of catalytic branching.

AB - We study the model of binary branching Brownian motion with spatially-inhomogeneous branching rate βδ0(·), where δ0(·) is the Dirac delta function and β is some positive constant. We show that the distribution of the rightmost particle centred about β/2 t converges to a mixture of Gumbel distributions according to a martingale limit. Our results form a natural extension to S. Lalley and T. Sellke [10] for the degenerate case of catalytic branching.

KW - Brownian motion

KW - Catalytic branching

KW - Local time

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UR - http://dx.doi.org/10.1214/16-ECP22

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DO - 10.1214/16-ECP22

M3 - Article

AN - SCOPUS:84994030723

SN - 1083-589X

VL - 21

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

M1 - Paper no. 70

ER -

Limiting distribution of the rightmost particle in catalytic branching Brownian motion

Abstract

Keywords

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