Fluctuations and moderate deviations for the mean fields of Hawkes processes

Fuqing Gao; Yunshi Gao; Lingjiong Zhu

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arXiv · 2307.15903

Fluctuations and moderate deviations for the mean fields of Hawkes processes

Fuqing Gao·Yunshi Gao·Lingjiong Zhu

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Abstract

The Hawkes process is a counting process that has self- and mutually-exciting features with many applications in various fields. In recent years, there have been many interests in the mean-field results of the Hawkes process and its extensions. It is known that the mean-field limit of a multivariate nonlinear Hawkes process is a time-inhomogeneous Poisson process. In this paper, we study the fluctuations for the mean fields and the large deviations associated with the fluctuations, i.e., the moderate deviations.

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Fuqing Gao, Yunshi Gao, Lingjiong Zhu. 2023-07-29. Fluctuations and moderate deviations for the mean fields of Hawkes processes. https://arxiv.org/abs/2307.15903

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