Critical Branching Brownian Motion with Killing

Steven P. Lalley; Bowei Zheng

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arXiv · 1507.02345

Critical Branching Brownian Motion with Killing

Steven P. Lalley·Bowei Zheng

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Abstract

We obtain sharp asymptotic estimates for hitting probabilities of a critical branching Brownian motion in one dimension with killing at 0 We also obtain sharp asymptotic formulas for the tail probabilities of the number of particles killed at 0. In the special case of double-or-nothing branching, we give exact formulas for both the hitting probabilities, in terms of elliptic functions, and the distribution of the number of killed particles.

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Steven P. Lalley, Bowei Zheng. 2015-07-09. Critical Branching Brownian Motion with Killing. https://arxiv.org/abs/1507.02345

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