We study a d-dimensional branching Brownian motion, 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 hits a trap,
asymptotically, in time.
This proves to be a rich problem, motivating the proof of a 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.
This is joint work with Mine Caglar and Mehmet Oz.