The almost-sure population growth rate in branching Brownian motion with a quadratic breeding potential

J Berestycki; E Brunet; J W Harris; Simon C Harris

doi:10.1016/j.spl.2010.05.011

The almost-sure population growth rate in branching Brownian motion with a quadratic breeding potential

J Berestycki
, E Brunet
, J W Harris
, Simon C Harris

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

7 Citations (SciVal)

225 Downloads (Pure)

Abstract

In this note we consider a branching Brownian motion (BBM) on R in which a particle at spatial position y splits into two at rate beta y(2), where beta > 0 is a constant. This is a critical breeding rate for BBM in the sense that the expected population size blows up in finite time while the population size remains finite, almost surely, for all time. We find an asymptotic for the almost-sure rate of growth of the population.

Original language	English
Pages (from-to)	1442-1446
Number of pages	5
Journal	Statistics & Probability Letters
Volume	80
Issue number	17-18
DOIs	https://doi.org/10.1016/j.spl.2010.05.011
Publication status	Published - 15 Sept 2010

Keywords

branching Brownian motion

Access to Document

10.1016/j.spl.2010.05.011

Harris_StatProbLet_2010_80_17-18_14442.pdf
This is the author’s version. A definitive version was subsequently published in Statistics & Probability Letters Volume 80, Issues 17-18, September 2010, DOI: 10.1016/j.spl.2010.05.011

Cite this

@article{c5baa41814d44ef4a92868d7940775c7,

title = "The almost-sure population growth rate in branching Brownian motion with a quadratic breeding potential",

abstract = "In this note we consider a branching Brownian motion (BBM) on R in which a particle at spatial position y splits into two at rate beta y(2), where beta > 0 is a constant. This is a critical breeding rate for BBM in the sense that the expected population size blows up in finite time while the population size remains finite, almost surely, for all time. We find an asymptotic for the almost-sure rate of growth of the population.",

keywords = "branching Brownian motion",

author = "J Berestycki and E Brunet and Harris, \{J W\} and Harris, \{Simon C\}",

year = "2010",

month = sep,

day = "15",

doi = "10.1016/j.spl.2010.05.011",

language = "English",

volume = "80",

pages = "1442--1446",

journal = "Statistics \& Probability Letters",

issn = "0167-7152",

publisher = "Elsevier B.V.",

number = "17-18",

}

TY - JOUR

T1 - The almost-sure population growth rate in branching Brownian motion with a quadratic breeding potential

AU - Berestycki, J

AU - Brunet, E

AU - Harris, J W

AU - Harris, Simon C

PY - 2010/9/15

Y1 - 2010/9/15

N2 - In this note we consider a branching Brownian motion (BBM) on R in which a particle at spatial position y splits into two at rate beta y(2), where beta > 0 is a constant. This is a critical breeding rate for BBM in the sense that the expected population size blows up in finite time while the population size remains finite, almost surely, for all time. We find an asymptotic for the almost-sure rate of growth of the population.

AB - In this note we consider a branching Brownian motion (BBM) on R in which a particle at spatial position y splits into two at rate beta y(2), where beta > 0 is a constant. This is a critical breeding rate for BBM in the sense that the expected population size blows up in finite time while the population size remains finite, almost surely, for all time. We find an asymptotic for the almost-sure rate of growth of the population.

KW - branching Brownian motion

UR - https://www.scopus.com/pages/publications/77954536266

UR - http://dx.doi.org/10.1016/j.spl.2010.05.011

U2 - 10.1016/j.spl.2010.05.011

DO - 10.1016/j.spl.2010.05.011

M3 - Article

SN - 0167-7152

VL - 80

SP - 1442

EP - 1446

JO - Statistics & Probability Letters

JF - Statistics & Probability Letters

IS - 17-18

ER -

The almost-sure population growth rate in branching Brownian motion with a quadratic breeding potential

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this