Abstract

We study binary branching Brownian motion in a bounded domain D of R^d satisfying certain regularity assumptions, in which particles are killed upon hitting the boundary dD. It was proved by Watanabe and Sevast’yanov that there is a critical value of the branching parameter beta above which the probability that the process survives for all time becomes strictly positive. For all beta less than or equal to this critical value, the process dies out almost surely. We offer a new proof of this result using certain martingales associated with the process, and further investigate the system at criticality. For a smooth domain, combining spine techniques with an asymptotic analysis of the FKPP equation allows us to prove an exact asymptotic for the probability of survival up to large time t. This is subject to the proof of a technical lemma, which we expect to be completed shortly.