论文标题
布朗尼分支运动的级联家族的极端过程
The extremal process of a cascading family of branching Brownian motion
论文作者
论文摘要
我们研究了布朗尼分支动作的层叠家族的极端过程的渐近行为。这是真实线上的粒子系统，因此每个粒子都具有其位置外的类型。 $ 1 $的类型颗粒根据布朗动议在实际线路上移动，并以$ 1 $的分支为$ 1 $ $ 1 $。此外，以$α$的价格，他们也生下了2美元的儿童。 $ 2 $的颗粒根据标准的布朗尼运动和分支机构以$ 1 $的价格移动，但不能诞生$ 1 $的后代。我们获得了$ 2 $的粒子的极端过程的渐近行为。
We study the asymptotic behaviour of the extremal process of a cascading family of branching Brownian motions. This is a particle system on the real line such that each particle has a type in addition to his position. Particles of type $1$ move on the real line according to Brownian motions and branch at rate $1$ into two children of type $1$. Furthermore, at rate $α$, they give birth to children too of type $2$. Particles of type $2$ move according to standard Brownian motion and branch at rate $1$, but cannot give birth to descendants of type $1$. We obtain the asymptotic behaviour of the extremal process of particles of type $2$.
