Conditional speed of branching Brownian motion, skeleton decomposition and application to random obstacles
Type :
Article
Publication Status :
published
Access :
restrictedAccess
Abstract
We 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.
Source :
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
Date :
2017
Publisher :
Institute of Mathematical Statistics
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