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
SN - 0167-7152
VL - 80
SP - 1442
EP - 1446
JO - Statistics & Probability Letters
JF - Statistics & Probability Letters
IS - 17-18
ER -