Fluctuations and moderate deviations for the mean fields of Hawkes processes

2023/07/29 by Gao, Fuqing, Gao, Yunshi, Zhu, Lingjiong
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2307.15903

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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