Large deviations and almost sure convergence for the extremes of branching Lévy processes
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918151530217472 |
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| author | Luo, Runjia Ren, Yan-Xia Song, Renming Zhang, Rui |
| author_facet | Luo, Runjia Ren, Yan-Xia Song, Renming Zhang, Rui |
| contents | In this paper, we investigate the asymptotic behavior of supercritical branching Markov processes $\{\mathbb{X}_t, t \ge0\}$ whose spatial motions are Lévy processes with regularly varying tails. Recently, Ren et al. [Appl. Probab. 61 (2024)] studied the weak convergence of the extremes of $\{\mathbb{X}_t, t \ge0\}$. In this paper, we establish the large deviation of $\{\mathbb{X}_t, t \ge0\}$ as well as some almost sure convergence results of the maximum of $\mathbb{X}_t$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25917 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large deviations and almost sure convergence for the extremes of branching Lévy processes Luo, Runjia Ren, Yan-Xia Song, Renming Zhang, Rui Probability In this paper, we investigate the asymptotic behavior of supercritical branching Markov processes $\{\mathbb{X}_t, t \ge0\}$ whose spatial motions are Lévy processes with regularly varying tails. Recently, Ren et al. [Appl. Probab. 61 (2024)] studied the weak convergence of the extremes of $\{\mathbb{X}_t, t \ge0\}$. In this paper, we establish the large deviation of $\{\mathbb{X}_t, t \ge0\}$ as well as some almost sure convergence results of the maximum of $\mathbb{X}_t$. |
| title | Large deviations and almost sure convergence for the extremes of branching Lévy processes |
| topic | Probability |
| url | https://arxiv.org/abs/2509.25917 |