Critical branching Brownian motion with absorption: survival probability

Abstract

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 $$-\sqrt{2}$$ . 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).