A Yaglom type asymptotic result for subcritical branching Brownian motion with absorption

Abstract

We consider a slightly subcritical branching Brownian motion with absorption, where particles move as Brownian motions with drift −2+2ɛ, undergo dyadic fission at rate 1, and are killed when they reach the origin. We obtain a Yaglom type asymptotic result, showing that the long run expected number of particles conditioned on survival grows exponentially as 1/ɛ as the process approaches criticality.