İskelet ayrışması, dallanan brown sürecinin koşullu hızı ve rassal engellere uygulama

We study a branching Brownian motion Z in R^d, among obstacles scattered according to a Poisson random measure. Obstacles are balls with constant radius and each one works as a trap for the whole process when hit by a particle. Considering a general offspring distribution for branching, we find the decay rate of the annealed probability that none of the particles of Z hits a trap, asymptotically in time t. This problem motivates the proof of a more general result about the speed of branching Brownian motion conditioned on non-extinction. On the way, we make use of the skeleton decomposition of the Galton-Watson process that underlies Z, and show that the skeleton alone is responsible for both the conditional speed of branching Brownian motion and the asymptotic decay rate of the annealed trap-avoiding probability of the system, that is, the non-skeleton particles play no role.