Tail probability of maximal displacement in critical and subcritical branching stable processes
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915232678412288 |
|---|---|
| author | Hou, Haojie Jiang, Yiyang Ren, Yan-Xia Song, Renming |
| author_facet | Hou, Haojie Jiang, Yiyang Ren, Yan-Xia Song, Renming |
| contents | 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, $γ\in (1, 2]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05540 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tail probability of maximal displacement in critical and subcritical branching stable processes Hou, Haojie Jiang, Yiyang Ren, Yan-Xia Song, Renming Probability 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, $γ\in (1, 2]$. |
| title | Tail probability of maximal displacement in critical and subcritical branching stable processes |
| topic | Probability |
| url | https://arxiv.org/abs/2504.05540 |