Escape Probabilities for Branching Brownian Motion Among Soft Obstacles

Jean-François Gall () and Amandine Véber ()
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Jean-François Gall: Université Paris-Sud
Amandine Véber: École Polytechnique

Journal of Theoretical Probability, 2012, vol. 25, issue 2, 505-535

Abstract: Abstract We derive asymptotics for the quenched probability that a critical branching Brownian motion killed at a small rate ε in Poissonian obstacles exits from 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 soft obstacles.

Keywords: Branching Brownian motion; Poissonian obstacles; Super-Brownian motion; Escape probability; Homogenization; Semilinear partial differential equation; 60K37; 60J80; 60J68 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10959-011-0343-x

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