Scaling limit for supercritical nearly unstable Hawkes processes with heavy tail
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913806448328704 |
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| author | Xu, Liping Zhang, An |
| author_facet | Xu, Liping Zhang, An |
| contents | In this paper, we establish the asymptotic behavior of {\it supercritical} nearly unstable Hawkes processes with a power law kernel. We find that, the Hawkes process in our context admits a similar equation to that in \cite{MR3563196} for {\it subcritical} case. In particular, the rescaled Hawkes process $(Z^n_{nt}/n^{2α})_{t\in[0,1]}$ converges in law to a kind of integrated fractional Cox Ingersoll Ross process with different coefficients from that in \cite{MR3563196}, as $n$ tends to infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16737 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scaling limit for supercritical nearly unstable Hawkes processes with heavy tail Xu, Liping Zhang, An Probability In this paper, we establish the asymptotic behavior of {\it supercritical} nearly unstable Hawkes processes with a power law kernel. We find that, the Hawkes process in our context admits a similar equation to that in \cite{MR3563196} for {\it subcritical} case. In particular, the rescaled Hawkes process $(Z^n_{nt}/n^{2α})_{t\in[0,1]}$ converges in law to a kind of integrated fractional Cox Ingersoll Ross process with different coefficients from that in \cite{MR3563196}, as $n$ tends to infinity. |
| title | Scaling limit for supercritical nearly unstable Hawkes processes with heavy tail |
| topic | Probability |
| url | https://arxiv.org/abs/2504.16737 |