Scaling limit for supercritical nearly unstable Hawkes processes with heavy tail

2025/04/23 by Liping Xu, An Zhang, Xu, Liping +1
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2504.16737

openalex publication_date 2025/04/23 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

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 \citeMR3563196 for \it subcritical case. In particular, the rescaled Hawkes process (Zⁿ_nt/n^2α)_t∈[0,1] converges in law to a kind of integrated fractional Cox Ingersoll Ross process with different coefficients from that in \citeMR3563196, as n tends to infinity.

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