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arXiv · 2504.05540

Tail probability of maximal displacement in critical and subcritical branching stable processes

Haojie Hou·Yiyang Jiang·Yan-Xia Ren·Renming Song
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Abstract

In this paper, we study critical and subcritical branching $α$-stable processes, $α\in (0, 2)$. We obtain the exact asymptotic behaviors of the tails of the maximal positions of all subcritical branching $α$-stable processes with positive jumps. In the case of subcritical branching spectrally negative $α$-stable processes, we obtain the exact asymptotic behaviors of the tails of the maximal positions under the assumption that the offspring distributions satisfy the $L\log L$ condition. For critical branching $α$-stable processes, we obtain the exact asymptotic behaviors of the tails under the assumption that the offspring distributions belong to the domain of attraction of a $γ$-distribution, $γ\in (1, 2]$.

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Haojie Hou, Yiyang Jiang, Yan-Xia Ren, Renming Song. 2025-04-07. Tail probability of maximal displacement in critical and subcritical branching stable processes. https://arxiv.org/abs/2504.05540

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