Critical branching Brownian motion with absorption: survival probability

@article{Berestycki2012CriticalBB,
  title={Critical branching Brownian motion with absorption: survival probability},
  author={Julien Berestycki and Nathanael Berestycki and Jason Schweinsberg},
  journal={Probability Theory and Related Fields},
  year={2012},
  volume={160},
  pages={489-520}
}
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 $$-\sqrt{2}$$-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 $$t$$t. These bounds improve upon results of Kesten (Stoch Process 7:9–47, 1978), and partially confirm… 

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