# Cumulants of Hawkes point processes

arXiv: https://arxiv.org/abs/1409.5353 · HTML: https://mlsanity.com/paper/1409.5353/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2014.

## Built on by (most cited first, 5 of 5)

- [Advances in Temporal Point Processes: Bayesian, Neural, and LLM Approaches](https://mlsanity.com/paper/2501.14291/) (2025)
- [Causal Representation Meets Stochastic Modeling under Generic Geometry](https://mlsanity.com/paper/2602.05033/) (2026)
- [An algorithm for the computation of joint Hawkes moments with exponential kernel](https://mlsanity.com/paper/2110.13649/) (2021)
- [Detecting Structural Shifts in Multivariate Hawkes Processes with Fr'echet Statistics](https://mlsanity.com/paper/2308.06769/) (2023)
- [Causal Structure Learning in Hawkes Processes with Complex Latent Confounder Networks](https://mlsanity.com/paper/2508.11727/) (2025)

## Abstract (arXiv)

We derive explicit, closed-form expressions for the cumulant densities of a multivariate, self-exciting Hawkes point process, generalizing a result of Hawkes in his earlier work on the covariance density and Bartlett spectrum of such processes. To do this, we represent the Hawkes process in terms of a Poisson cluster process and show how the cumulant density formulas can be derived by enumerating all possible "family trees", representing complex interactions between point events. We also consider the problem of computing the integrated cumulants, characterizing the average measure of correlated activity between events of different types, and derive the relevant equations.