Publication: Conditional speed of branching brownian motion, skeleton decomposition and application to random obstacles
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Englander, Janos
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NO
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Abstract
We 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.
Source
Publisher
Institute Henri Poincaré (IHP)
Subject
Mathematics, Statistics and probability
Citation
Has Part
Source
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
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DOI
10.1214/16-AIHP739