Escape probabilities for branching Brownian motion among mild obstacles

Jean-Francois Le Gall; Amandine Veber

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arXiv · 1003.3726

Escape probabilities for branching Brownian motion among mild obstacles

Jean-Francois Le Gall·Amandine Veber

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Abstract

We derive asymptotics for the quenched probability that a critical branching Brownian motion killed at a small rate in Poissonian obstacles exits a large domain. Results are formulated in terms of the solution to a semilinear partial differential equation with singular boundary conditions. The proofs depend on a quenched homogenization theorem for branching Brownian motion among mild obstacles.

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Jean-Francois Le Gall, Amandine Veber. 2010-03-19. Escape probabilities for branching Brownian motion among mild obstacles. https://arxiv.org/abs/1003.3726

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