Loglinear Hawkes processes
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866908450520301568 |
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| author | Bielecki, Tomasz R. Jakubowski, Jacek Kirchner, Matthias Niewęgłowski, Mariusz |
| author_facet | Bielecki, Tomasz R. Jakubowski, Jacek Kirchner, Matthias Niewęgłowski, Mariusz |
| contents | This paper discusses a special class of nonlinear Hawkes processes, where the rate function is the exponential function. We call these processes loglinear Hawkes processes. In the main theorem, we give sufficient conditions for explosion and nonexplosion that cover a large class of practically relevant memory functions. We also investigate stability. In particular, we show that for nonpositive memory functions the loglinear Hawkes process is stable. The paper aims at providing a theoretical basis for further research and applications of these processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11265 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Loglinear Hawkes processes Bielecki, Tomasz R. Jakubowski, Jacek Kirchner, Matthias Niewęgłowski, Mariusz Probability This paper discusses a special class of nonlinear Hawkes processes, where the rate function is the exponential function. We call these processes loglinear Hawkes processes. In the main theorem, we give sufficient conditions for explosion and nonexplosion that cover a large class of practically relevant memory functions. We also investigate stability. In particular, we show that for nonpositive memory functions the loglinear Hawkes process is stable. The paper aims at providing a theoretical basis for further research and applications of these processes. |
| title | Loglinear Hawkes processes |
| topic | Probability |
| url | https://arxiv.org/abs/2507.11265 |