We consider a slightly subcritical branching Brownian motion with absorption, where particles move as Brownian motions with drift $-\sqrt{2+2\epsilon }$, 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 $1∕\sqrt{\epsilon }$ as the process approaches criticality.

中文翻译：

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带吸收的亚临界分支布朗运动的 Yaglom 型渐近结果

我们考虑了一个带有吸收的稍微亚临界的分支布朗运动，其中粒子随着布朗运动的漂移而移动 $-\sqrt{2+2\epsilon }$，以速率 1 进行二元裂变，并在到达原点时被杀死。我们获得了 Yaglom 类型的渐近结果，表明以生存为条件的长期预期粒子数呈指数增长$1∕\sqrt{\epsilon }$ 随着过程接近临界点。