Department of Mathematics2024-11-0920170246-020310.1214/16-AIHP7392-s2.0-85018824809https://hdl.handle.net/20.500.14288/1220We study a branching Brownian motion Z in Rd, 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 Z hits a trap, asymptotically in time t. 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.pdfMathematicsStatistics and probabilityJournal Articlehttps://doi.org/10.1214/16-AIHP739399817300014Q2NOIR01222