Explicit correlations for the Hawkes processes

TL;DR

This paper derives explicit formulas for the correlation structure of Hawkes processes and their intensities, advancing theoretical understanding using Poisson embedding and Malliavin calculus techniques.

Contribution

It provides the first exact and explicit correlation expressions for general Hawkes processes, filling a key gap in the literature.

Findings

Explicit correlation formulas for Hawkes processes and intensities

Methodology based on Poisson imbedding and Malliavin calculus

Enhances theoretical analysis of Hawkes processes

Abstract

In this paper we fill a gap in the literature by providing exact and explicit expressions for the correlation of general Hawkes processes together with its intensity process. Our methodology relies on the Poisson imbedding representation and on recent findings on Malliavin calculus and pseudo-chaotic representation for counting processes.