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Article Dans Une Revue Probability Theory and Related Fields Année : 2014

Critical branching Brownian motion with absorption: survival probability

Résumé

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 -root 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).

Dates et versions

hal-01092743 , version 1 (09-12-2014)

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J. Berestycki, N. Berestycki, J. Schweinsberg. Critical branching Brownian motion with absorption: survival probability. Probability Theory and Related Fields, 2014, 160 (3-4), pp.489-520. ⟨10.1007/s00440-013-0533-9⟩. ⟨hal-01092743⟩
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