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 - http://www.scopus.com/inward/record.url?scp=77954536266&partnerID=8YFLogxK

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

VL - 80

SP - 1442

EP - 1446

JO - Statistics & Probability Letters

JF - Statistics & Probability Letters

SN - 0167-7152

IS - 17-18

ER -