More on the asymptotic behaviour of moments of branching Markov processes
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866929693191569408 |
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| author | Dean, Christopher B. C. Horton, Emma |
| author_facet | Dean, Christopher B. C. Horton, Emma |
| contents | Consider a branching Markov process, $X = (X(t), t \ge 0)$, with non-local branching mechanism. Studying the asymptotic behaviour of the moments of X has recently received attention in the literature [6, 7] due to the importance of these results in understanding the underlying genealogical structure of $X$. In this article, we generalise the results of [7] to allow for a non-simple leading eigenvalue and to also study the higher order fluctuations of the moments of $X$. These results will be useful for proving central limit theorems and extending well-known LLN results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_19268 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | More on the asymptotic behaviour of moments of branching Markov processes Dean, Christopher B. C. Horton, Emma Probability Consider a branching Markov process, $X = (X(t), t \ge 0)$, with non-local branching mechanism. Studying the asymptotic behaviour of the moments of X has recently received attention in the literature [6, 7] due to the importance of these results in understanding the underlying genealogical structure of $X$. In this article, we generalise the results of [7] to allow for a non-simple leading eigenvalue and to also study the higher order fluctuations of the moments of $X$. These results will be useful for proving central limit theorems and extending well-known LLN results. |
| title | More on the asymptotic behaviour of moments of branching Markov processes |
| topic | Probability |
| url | https://arxiv.org/abs/2501.19268 |