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

J Berestycki; E Brunet; JW Harris; SC 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, JW Harris, SC Harris

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

7 Citations (Scopus)

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 βy2, where β>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.

Translated title of the contribution	The almost-sure population growth rate in branching Brownian motion with a quadratic breeding potential
Original language	English
Pages (from-to)	1442 - 1446
Number of pages	5
Journal	Statistics and Probability Letters
Volume	80, issues 17-18
DOIs	https://doi.org/10.1016/j.spl.2010.05.011
Publication status	Published - Sep 2010

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Publisher: Elsevier

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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 βy2, where β>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.",

author = "J Berestycki and E Brunet and JW Harris and SC Harris",

note = "Publisher: Elsevier",

year = "2010",

month = sep,

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

language = "English",

volume = "80, issues 17-18",

pages = "1442 -- 1446",

journal = "Statistics and Probability Letters",

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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, JW

AU - Harris, SC

N1 - Publisher: Elsevier

PY - 2010/9

Y1 - 2010/9

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 βy2, where β>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 βy2, where β>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.

U2 - 10.1016/j.spl.2010.05.011

DO - 10.1016/j.spl.2010.05.011

M3 - Article (Academic Journal)

VL - 80, issues 17-18

SP - 1442

EP - 1446

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

ER -

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

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