Gaussian approximation of nonlinear Hawkes processes

TL;DR

This paper establishes a Gaussian approximation framework for nonlinear Hawkes processes, offering quantitative central limit theorems by analyzing the first chaos of point processes with stochastic intensity.

Contribution

It introduces a general Gaussian bound for the first chaos of point processes and applies it to nonlinear Hawkes processes, providing new quantitative CLTs.

Findings

Gaussian bounds for the first chaos of point processes

Quantitative central limit theorems for nonlinear Hawkes processes

Enhanced understanding of stochastic intensity in point processes

Abstract

We give a general Gaussian bound for the first chaos (or innovation) of point processes with stochastic intensity constructed by embedding in a bivariate Poisson process. We apply the general result to nonlinear Hawkes processes, providing quantitative central limit theorems.