Hawkes Models And Their Applications
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910450516492288 |
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| author | Laub, Patrick J. Lee, Young Pollett, Philip K. Taimre, Thomas |
| author_facet | Laub, Patrick J. Lee, Young Pollett, Philip K. Taimre, Thomas |
| contents | The Hawkes process is a model for counting the number of arrivals to a system which exhibits the self-exciting property - that one arrival creates a heightened chance of further arrivals in the near future. The model, and its generalizations, have been applied in a plethora of disparate domains, though two particularly developed applications are in seismology and in finance. As the original model is elegantly simple, generalizations have been proposed which: track marks for each arrival, are multivariate, have a spatial component, are driven by renewal processes, treat time as discrete, and so on. This paper creates a cohesive review of the traditional Hawkes model and the modern generalizations, providing details on their construction, simulation algorithms, and giving key references to the appropriate literature for a detailed treatment. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10527 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hawkes Models And Their Applications Laub, Patrick J. Lee, Young Pollett, Philip K. Taimre, Thomas Methodology Probability Applications The Hawkes process is a model for counting the number of arrivals to a system which exhibits the self-exciting property - that one arrival creates a heightened chance of further arrivals in the near future. The model, and its generalizations, have been applied in a plethora of disparate domains, though two particularly developed applications are in seismology and in finance. As the original model is elegantly simple, generalizations have been proposed which: track marks for each arrival, are multivariate, have a spatial component, are driven by renewal processes, treat time as discrete, and so on. This paper creates a cohesive review of the traditional Hawkes model and the modern generalizations, providing details on their construction, simulation algorithms, and giving key references to the appropriate literature for a detailed treatment. |
| title | Hawkes Models And Their Applications |
| topic | Methodology Probability Applications |
| url | https://arxiv.org/abs/2405.10527 |