Survival of branching Brownian motion in a uniform trap field

We study a branching Brownian motion Z evolving in Rd, where a uniform field of Poissonian traps are present. We consider a general offspring distribution for Z and find the asymptotic decay rate of the annealed survival probability, conditioned on non-extinction. The method of proof is to use a skeleton decomposition for the Galton-Watson process underlying Z and to show that the particles of finite line of descent do not contribute to the survival asymptotics. This work is a follow-up to Öz and Çağlar (2013) and solves the problem considered therein completely.