Berestycki, J., Brunet, E., Harris, J. W. and Harris, S. C., 2010. The almost-sure population growth rate in branching Brownian motion with a quadratic breeding potential. Statistics & Probability Letters, 80 (17-18), pp. 1442-1446.
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.
|Item Type ||Articles|
|Creators||Berestycki, J., Brunet, E., Harris, J. W. and Harris, S. C.|
|Uncontrolled Keywords||branching brownian motion|
|Departments||Faculty of Science > Mathematical Sciences|
|Publisher Statement||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|
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