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

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

16 Citations (SciVal)

194 Downloads (Pure)

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

Access to Document

10.1214/16-ECP22Licence: CC BY

Published VersionFinal published version, 247 KBLicence: CC BY

Cite this

@article{8a529d7739cd4d9a8b5ee929c1b850aa,

title = "Limiting distribution of the rightmost particle in catalytic branching Brownian motion",

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.",

keywords = "Brownian motion, Catalytic branching, Local time",

author = "Sergey Bocharov and Harris, \{Simon C.\}",

year = "2016",

month = oct,

day = "4",

doi = "10.1214/16-ECP22",

language = "English",

volume = "21",

journal = "Electronic Communications in Probability",

issn = "1083-589X",

publisher = "Institute of Mathematical Statistics",

}

TY - JOUR

T1 - Limiting distribution of the rightmost particle in catalytic branching Brownian motion

AU - Bocharov, Sergey

AU - Harris, Simon C.

PY - 2016/10/4

Y1 - 2016/10/4

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

UR - http://www.scopus.com/inward/record.url?scp=84994030723&partnerID=8YFLogxK

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

U2 - 10.1214/16-ECP22

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

Access to Document

Other files and links

Fingerprint

Cite this