# Hawkes Processes with Stochastic Excitations

arXiv: https://arxiv.org/abs/1609.06831 · HTML: https://mlsanity.com/paper/1609.06831/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Sep 2016.

## Built on by (most cited first, 4 of 4)

- [Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equations](https://mlsanity.com/paper/2206.08311/) (2022)
- [Scalable Marked Point Processes for Exchangeable and Non-Exchangeable Event Sequences](https://mlsanity.com/paper/2105.14574/) (2021)
- [A neural network based model for multi-dimensional nonlinear Hawkes processes](https://mlsanity.com/paper/2303.03073/) (2023)
- [Unsupervised Event Outlier Detection in Continuous Time](https://mlsanity.com/paper/2411.16427/) (2024)

## Abstract (arXiv)

We propose an extension to Hawkes processes by treating the levels of self-excitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate each other with correlated levels of contagion. We generalize a recent algorithm for simulating draws from Hawkes processes whose levels of excitation are stochastic processes, and propose a hybrid Markov chain Monte Carlo approach for model fitting. Our sampling procedure scales linearly with the number of required events and does not require stationarity of the point process. A modular inference procedure consisting of a combination between Gibbs and Metropolis Hastings steps is put forward. We recover expectation maximization as a special case. Our general approach is illustrated for contagion following geometric Brownian motion and exponential Langevin dynamics.