Law of iterated logarithm for supercritical non-symmetric branching Markov process
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915668991934464 |
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| author | Hou, Haojie Ren, Yan-Xia Song, Renming |
| author_facet | Hou, Haojie Ren, Yan-Xia Song, Renming |
| contents | Let $\{(X_t)_{t\geq 0}, \mathbb{P}_{δ_x}, x\in E\}$ be a supercritical branching Markov process (which is not necessary symmetric) on a locally compact metric measure space $(E,μ)$ with spatially dependent local branching mechanism. Under some assumptions on the semigroup of the spatial motion, we first prove law of iterated logarithm type results for $\langle f, X_t\rangle$ under the second moment condition on the branching mechanism, where $f$ is a linear combination of eigenfunctions of the mean semigroup $\{T_t, t\geq0\}$ of $X$. Then we prove law of iterated logarithm type results for $\langle f, X_t\rangle$ under the fourth moment condition, where $f$ belongs to a larger class of functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12691 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Law of iterated logarithm for supercritical non-symmetric branching Markov process Hou, Haojie Ren, Yan-Xia Song, Renming Probability Let $\{(X_t)_{t\geq 0}, \mathbb{P}_{δ_x}, x\in E\}$ be a supercritical branching Markov process (which is not necessary symmetric) on a locally compact metric measure space $(E,μ)$ with spatially dependent local branching mechanism. Under some assumptions on the semigroup of the spatial motion, we first prove law of iterated logarithm type results for $\langle f, X_t\rangle$ under the second moment condition on the branching mechanism, where $f$ is a linear combination of eigenfunctions of the mean semigroup $\{T_t, t\geq0\}$ of $X$. Then we prove law of iterated logarithm type results for $\langle f, X_t\rangle$ under the fourth moment condition, where $f$ belongs to a larger class of functions. |
| title | Law of iterated logarithm for supercritical non-symmetric branching Markov process |
| topic | Probability |
| url | https://arxiv.org/abs/2505.12691 |