Moments of additive martingales of branching Lévy processes and applications
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909783161831424 |
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| author | Ren, Yan-Xia Song, Renming Zhang, Rui |
| author_facet | Ren, Yan-Xia Song, Renming Zhang, Rui |
| contents | Let $W_t(θ)$ be the Biggins martingale of a supercritical branching Lévy process with non-local branching mechanism, and denote by $W_\infty(θ)$ its limit. In this paper, we first study moment properties of $W_t(θ)$ and $W_\infty(θ)$, and the tail behavior of $W_\infty(θ)$. We then apply these results to establish central limit theorems for $W_t(θ)-W_\infty(θ)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09188 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Moments of additive martingales of branching Lévy processes and applications Ren, Yan-Xia Song, Renming Zhang, Rui Probability Let $W_t(θ)$ be the Biggins martingale of a supercritical branching Lévy process with non-local branching mechanism, and denote by $W_\infty(θ)$ its limit. In this paper, we first study moment properties of $W_t(θ)$ and $W_\infty(θ)$, and the tail behavior of $W_\infty(θ)$. We then apply these results to establish central limit theorems for $W_t(θ)-W_\infty(θ)$. |
| title | Moments of additive martingales of branching Lévy processes and applications |
| topic | Probability |
| url | https://arxiv.org/abs/2509.09188 |