Limit theorems for non linear (compound marked) Hawkes processes

TL;DR

This paper establishes a central limit theorem and convergence rate bounds for non-linear compound marked Hawkes processes, advancing theoretical understanding of their asymptotic behavior.

Contribution

It derives a CLT and provides convergence rate bounds for non-linear compound marked Hawkes processes, filling a gap in the existing literature.

Findings

Established a CLT for the process

Provided an upper bound on convergence rate

Used discretization to analyze process convergence

Abstract

In this article, we fill a gap in the literature on Hawkes processes. In particular, we derive a CLT for a non linear compound marked Hawkes process. We also provide an upper bound on the convergence rate using the functional 1-Wasserstein distance. This result is obtained by discretizing the time line and reducing the problem to the quantification of the distance between finite marginal vectors, as well as between the discretized process and the original one.