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A Yaglom type asymptotic result for subcritical branching Brownian motion with absorption
Stochastic Processes and their Applications ( IF 1.4 ) Pub Date : 2021-07-28 , DOI: 10.1016/j.spa.2021.07.009 Jiaqi Liu 1
中文翻译:
带吸收的亚临界分支布朗运动的 Yaglom 型渐近结果
更新日期:2021-08-07
Stochastic Processes and their Applications ( IF 1.4 ) Pub Date : 2021-07-28 , DOI: 10.1016/j.spa.2021.07.009 Jiaqi Liu 1
Affiliation
We consider a slightly subcritical branching Brownian motion with absorption, where particles move as Brownian motions with drift , 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 as the process approaches criticality.
中文翻译:
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 ,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 随着过程接近临界点。