Critical branching Brownian motion with absorption: survival probability

We consider branching Brownian motion on the real line with absorption at zero, in which particles move according to independent Brownian motions with the critical drift of - 2 . Kesten (Stoch Process 7:9–47, 1978 ) showed that almost surely this process eventually dies out. Here we obtain upper and...

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Bibliographic Details
Published in:Probability theory and related fields 2014-12, Vol.160 (3-4), p.489-520
Main Authors: Berestycki, Julien, Berestycki, Nathanaël, Schweinsberg, Jason
Format: Article
Language:English
Subjects:
Absorption
Brownian motion
Critical phenomena
Dies
Drift
Economics
Extinction
Finance
Insurance
Lower bounds
Management
Mathematical analysis
Mathematical and Computational Biology
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Partial differential equations
Probability
Probability theory
Probability Theory and Stochastic Processes
Quantitative Finance
Statistics for Business
Studies
Survival
Survival analysis
Texts
Theoretical
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Summary:We consider branching Brownian motion on the real line with absorption at zero, in which particles move according to independent Brownian motions with the critical drift of - 2 . Kesten (Stoch Process 7:9–47, 1978 ) showed that almost surely this process eventually dies out. Here we obtain upper and lower bounds on the probability that the process survives until some large time t . These bounds improve upon results of Kesten (Stoch Process 7:9–47, 1978 ), and partially confirm nonrigorous predictions of Derrida and Simon (EPL 78:60006, 2007 ).
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-013-0533-9