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

2025/04/07 by Haojie Hou, Yiyang Jiang, Hou, Haojie +5 · 1 citation
Environmental Science · Mathematics · #Ecosystem dynamics and resilience #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2504.05540

openalex publication_date 2025/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study critical and subcritical branching α-stable processes, α∈ (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 Llog 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∈ (1, 2].

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