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arXiv · 2004.02084

A Yaglom type asymptotic result for subcritical branching Brownian motion with absorption

Jiaqi Liu
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Abstract

We consider a slightly subcritical branching Brownian motion with absorption, where particles move as Brownian motions with drift $-\sqrt{2+2\varepsilon}$, undergo dyadic fission at rate $1$, and are killed when they reach the origin. We obtain a Yaglom type asymptotic result, showing that the long run expected number of particles conditioned on survival grows exponentially as $1/\sqrt{\varepsilon}$ as the process approaches criticality.

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Jiaqi Liu. 2020-04-05. A Yaglom type asymptotic result for subcritical branching Brownian motion with absorption. https://doi.org/10.1016/j.spa.2021.07.009

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