Weak convergence of the extremes of branching L\'evy processes with regularly varying tails

Yan-Xia Ren; Renming Song; Rui Zhang

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arXiv · 2210.06130

Weak convergence of the extremes of branching L\'evy processes with regularly varying tails

Yan-Xia Ren·Renming Song·Rui Zhang

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Abstract

In this paper, we study the weak convergence of the extremes of supercritical branching L\'evy processes $\{\mathbb{X}_t, t \ge0\}$ whose spatial motions are L\'evy 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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BibTeX RIS

Yan-Xia Ren, Renming Song, Rui Zhang. 2022-10-12. Weak convergence of the extremes of branching L\'evy processes with regularly varying tails. https://arxiv.org/abs/2210.06130

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