论文标题
亚临界分支布朗尼运动带吸收的亚临界分支的Yaglom型渐近结果
A Yaglom type asymptotic result for subcritical branching Brownian motion with absorption
论文作者
论文摘要
我们考虑了带有吸收的略微亚临界分支的布朗运动，其中颗粒作为带有漂移$ - \ sqrt {2+2 \ 2 \ varepsilon} $的布朗运动移动，以$ 1 $的价格进行二元裂变，并在达到原点时被杀死。我们获得了Yaglom类型的渐近结果，表明以生存条件为条件的长期预期粒子呈指数增长为$ 1/\ sqrt {\ varepsilon} $，因为该过程接近关键。
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.
