Critical Branching Brownian Motion with Killing
Steven P. Lalley, Bowei Zheng
TL;DR
This paper derives precise asymptotic estimates for hitting probabilities and the distribution of killed particles in a critical branching Brownian motion with killing at zero, including exact formulas for special cases.
Contribution
It provides new sharp asymptotic estimates and exact formulas for hitting probabilities and killed particle distributions in critical branching Brownian motion with killing.
Findings
Sharp asymptotic estimates for hitting probabilities
Asymptotic formulas for tail probabilities of killed particles
Exact formulas involving elliptic functions for double-or-nothing branching
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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Taxonomy
TopicsStochastic processes and statistical mechanics · Probability and Risk Models · Stochastic processes and financial applications