Long-time asymptotics for multivariate Hawkes processes with long-range interactions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918375339327488 |
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| author | Belmabrouk, Nadia |
| author_facet | Belmabrouk, Nadia |
| contents | We study a multivariate Hawkes process with long-range interactions, where the interaction strength decays as a power-law in the distance of the particles with exponent $1+α.$ Our main focus is on the long-time asymptotic behavior of the system. The proofs of our results combine techniques developed for short-range interactions, properties of $α$-stable laws, and a Tauberian theorem. This model is more intricate and realistic for some applications, such as neural networks, where long-range connections are present. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05853 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Long-time asymptotics for multivariate Hawkes processes with long-range interactions Belmabrouk, Nadia Probability We study a multivariate Hawkes process with long-range interactions, where the interaction strength decays as a power-law in the distance of the particles with exponent $1+α.$ Our main focus is on the long-time asymptotic behavior of the system. The proofs of our results combine techniques developed for short-range interactions, properties of $α$-stable laws, and a Tauberian theorem. This model is more intricate and realistic for some applications, such as neural networks, where long-range connections are present. |
| title | Long-time asymptotics for multivariate Hawkes processes with long-range interactions |
| topic | Probability |
| url | https://arxiv.org/abs/2603.05853 |