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

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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 languageEnglish
Pages (from-to)1442-1446
Number of pages5
JournalStatistics & Probability Letters
Volume80
Issue number17-18
DOIs
Publication statusPublished - 15 Sep 2010

Keywords

  • branching Brownian motion

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