Scaling limit for supercritical nearly unstable Hawkes processes with heavy tail

Liping Xu; An Zhang

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arXiv · 2504.16737

Scaling limit for supercritical nearly unstable Hawkes processes with heavy tail

Liping Xu·An Zhang

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Abstract

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 $(Z^n_{nt}/n^{2\alpha})_{t\in[0,1]}$ 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.

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Liping Xu, An Zhang. 2025-04-23. Scaling limit for supercritical nearly unstable Hawkes processes with heavy tail. https://arxiv.org/abs/2504.16737

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