Öz, MehmetÇağlar, M.Engländer, J.2017-06-172017-06-1720170246-0203https://doi.org/10.1214/16-AIHP739http://hdl.handle.net/10679/5359We study a branching Brownian motion ZZ in RdRd, among obstacles scattered according to a Poisson random measure with a radially decaying intensity. Obstacles are balls with constant radius and each one works as a trap for the whole motion when hit by a particle. Considering a general offspring distribution, we derive the decay rate of the annealed probability that none of the particles of ZZ hits a trap, asymptotically in time tt. This proves to be a rich problem motivating the proof of a more general result about the speed of branching Brownian motion conditioned on non-extinction. We provide an appropriate “skeleton” decomposition for the underlying Galton–Watson process when supercritical and show that the “doomed” particles do not contribute to the asymptotic decay rate.engrestrictedAccessarticle00039981730001410.1214/16-AIHP739Branching Brownian motionPoissonian trapsRandom environmentHard obstaclesRightmost particle2-s2.0-85018824809