论文标题
分支的极端分支莱维过程的融合较弱，定期变化的尾巴
Weak convergence of the extremes of branching Lévy processes with regularly varying tails
论文作者
论文摘要
在本文中，我们研究了超临界分支lévy过程的极端趋势，$ \ {\ mathbb {x} _t，t \ ge0 \} $，其空间运动是lévy过程，其定期变化。结果与分支布朗尼运动的情况截然不同。我们证明，在正确重新归一化时，$ \ mathbb {x} _t $会弱收敛。结果，我们获得了$ \ mathbb {x} _t $的订单统计信息的限制定理。
In this paper, we study the weak convergence of the extremes of supercritical branching Lévy processes $\{\mathbb{X}_t, t \ge0\}$ whose spatial motions are Lévy processes with regularly varying tails. The result is drastically different from the case of branching Brownian motions. We prove that, when properly renormalized, $\mathbb{X}_t$ converges weakly. As a consequence, we obtain a limit theorem for the order statistics of $\mathbb{X}_t$.
