Weak convergence of the extremes of branching Lévy processes with regularly varying tails

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY Journal of Applied Probability Pub Date : 2023-12-06 DOI:10.1017/jpr.2023.103

Yan-xia Ren, Renming Song, Rui Zhang

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引用次数: 1

Abstract

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

$\mathbb{X}_t$

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具有规则变化尾的分支lsamvy过程的极端的弱收敛性

研究了超临界分支lsamvy过程$\{\mathbb{X}_t, t \ge0\}$的极值的弱收敛性，这些过程的空间运动是尾部有规则变化的lsamvy过程。其结果与分支布朗运动的情况截然不同。我们证明，当适当地重整时，$\mathbb{X}_t$是弱收敛的。因此，我们得到了$\mathbb{X}_t$阶统计量的一个极限定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Applied Probability 数学-统计学与概率论

CiteScore

1.50

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Applied Probability is the oldest journal devoted to the publication of research in the field of applied probability. It is an international journal published by the Applied Probability Trust, and it serves as a companion publication to the Advances in Applied Probability. Its wide audience includes leading researchers across the entire spectrum of applied probability, including biosciences applications, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used. A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.