Vague convergence and method of moments for random metric measure spaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909436278210560 |
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| author | Foutel-Rodier, Félix |
| author_facet | Foutel-Rodier, Félix |
| contents | We introduce a notion of vague convergence for random marked metric measure spaces. Our main result shows that convergence of the moments of order $k \ge 1$ of a random marked metric measure space is sufficient to obtain its vague convergence in the Gromov-weak topology. This result improves on previous methods of moments that also require convergence of the moment of order $k=0$, which in applications to critical branching processes amounts to estimating a survival probability. We also derive two useful companion results, namely a continuous mapping theorem and an approximation theorem for vague convergence of random marked metric measure spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05097 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Vague convergence and method of moments for random metric measure spaces Foutel-Rodier, Félix Probability We introduce a notion of vague convergence for random marked metric measure spaces. Our main result shows that convergence of the moments of order $k \ge 1$ of a random marked metric measure space is sufficient to obtain its vague convergence in the Gromov-weak topology. This result improves on previous methods of moments that also require convergence of the moment of order $k=0$, which in applications to critical branching processes amounts to estimating a survival probability. We also derive two useful companion results, namely a continuous mapping theorem and an approximation theorem for vague convergence of random marked metric measure spaces. |
| title | Vague convergence and method of moments for random metric measure spaces |
| topic | Probability |
| url | https://arxiv.org/abs/2402.05097 |