Weak convergence of the extremes of branching Lvy processes with regularly varying tails
JOURNAL OF APPLIED PROBABILITY(2023)
摘要
We study the weak convergence of the extremes of supercritical branching Levy processes $\{\mathbb{X}_t, t \ge0\}$ whose spatial motions are Levy 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 $\mathbb{X}_t$.
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关键词
Branching Levy process,extremal process,regularly varying,rightmost position
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