Large deviations for the mean-field limit of Hawkes processes

Fuqing Gao; Lingjiong Zhu

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arXiv · 2301.07585

Large deviations for the mean-field limit of Hawkes processes

Fuqing Gao·Lingjiong Zhu

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Abstract

Hawkes processes are a class of simple point processes whose intensity depends on the past history, and is in general non-Markovian. Limit theorems for Hawkes processes in various asymptotic regimes have been studied in the literature. In this paper, we study a multidimensional nonlinear Hawkes process in the asymptotic regime when the dimension goes to infinity, whose mean-field limit is a time-inhomogeneous Poisson process, and our main result is a large deviation principle for the mean-field limit.

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Fuqing Gao, Lingjiong Zhu. 2023-01-18. Large deviations for the mean-field limit of Hawkes processes. https://arxiv.org/abs/2301.07585

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