Invertibility of functionals of the Poisson process and applications
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912992771178496 |
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| author | Coutin, Laure Decreusefond, Laurent |
| author_facet | Coutin, Laure Decreusefond, Laurent |
| contents | Following previous investigations by {Ü}st{ü}nel [22] about the invertibility of some transformations on the Wiener space, we find some entropic conditions under which a random change of time is invertible on the Poisson space. As a consequence, we provide a new construction of Hawkes processes. We also establish a new variational representation of the entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_02887 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Invertibility of functionals of the Poisson process and applications Coutin, Laure Decreusefond, Laurent Probability Following previous investigations by {Ü}st{ü}nel [22] about the invertibility of some transformations on the Wiener space, we find some entropic conditions under which a random change of time is invertible on the Poisson space. As a consequence, we provide a new construction of Hawkes processes. We also establish a new variational representation of the entropy. |
| title | Invertibility of functionals of the Poisson process and applications |
| topic | Probability |
| url | https://arxiv.org/abs/2307.02887 |