Translator Disclaimer
February 2022 Mean field limits for interacting Hawkes processes in a diffusive regime
Xavier Erny, Eva Löcherbach, Dasha Loukianova
Author Affiliations +
Bernoulli 28(1): 125-149 (February 2022). DOI: 10.3150/21-BEJ1335

Abstract

We consider a sequence of systems of Hawkes processes having mean field interactions in a diffusive regime. The stochastic intensity of each process is a solution of a stochastic differential equation driven by N independent Poisson random measures. We show that, as the number of interacting components N tends to infinity, this intensity converges in distribution in the Skorokhod space to a CIR-type diffusion. Moreover, we prove the convergence in distribution of the Hawkes processes to the limit point process having the limit diffusion as intensity. To prove the convergence results, we use analytical technics based on the convergence of the associated infinitesimal generators and Markovian semigroups.

Citation

Download Citation

Xavier Erny. Eva Löcherbach. Dasha Loukianova. "Mean field limits for interacting Hawkes processes in a diffusive regime." Bernoulli 28 (1) 125 - 149, February 2022. https://doi.org/10.3150/21-BEJ1335

Information

Received: 1 November 2019; Revised: 1 November 2020; Published: February 2022
First available in Project Euclid: 10 November 2021

Digital Object Identifier: 10.3150/21-BEJ1335

Keywords: mean field interaction , Multivariate nonlinear Hawkes processes , Piecewise deterministic Markov processes

Rights: Copyright © 2022 ISI/BS

JOURNAL ARTICLE
25 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.28 • No. 1 • February 2022
Back to Top