Escape probabilities for branching Brownian motion among mild obstacles

Details Escape probabilities for branching Brownian motion among mild obstacles Escape probabilities for branching Brownian motion among mild obstacles

2010-03-19

arxiv.org/abs/1003.3726v2

Mathematics

Probability

24 pages, to appear in Journal of Theoretical Probability

Scientific paper

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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