Tail asymptotics and precise large deviations for some Poisson cluster processes
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866915726789443584 |
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| author | Baeriswyl, Fabien Chavez-Demoulin, Valérie Wintenberger, Olivier |
| author_facet | Baeriswyl, Fabien Chavez-Demoulin, Valérie Wintenberger, Olivier |
| contents | We study the tail asymptotics of two functionals (the maximum and the sum of the marks) of a generic cluster in two sub-models of the marked Poisson cluster process, namely the renewal Poisson cluster process and the Hawkes process. Under the hypothesis that the governing components of the processes are regularly varying, we extend results due to [18] and [5] notably, relying on Karamata's Tauberian Theorem to do so. We use these asymptotics to derive precise large deviation results in the fashion of [30] for the above-mentioned processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_09705 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tail asymptotics and precise large deviations for some Poisson cluster processes Baeriswyl, Fabien Chavez-Demoulin, Valérie Wintenberger, Olivier Probability We study the tail asymptotics of two functionals (the maximum and the sum of the marks) of a generic cluster in two sub-models of the marked Poisson cluster process, namely the renewal Poisson cluster process and the Hawkes process. Under the hypothesis that the governing components of the processes are regularly varying, we extend results due to [18] and [5] notably, relying on Karamata's Tauberian Theorem to do so. We use these asymptotics to derive precise large deviation results in the fashion of [30] for the above-mentioned processes. |
| title | Tail asymptotics and precise large deviations for some Poisson cluster processes |
| topic | Probability |
| url | https://arxiv.org/abs/2304.09705 |