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


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.


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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


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

MathSciNet: MR4337700
zbMATH: 1490.60122
Digital Object Identifier: 10.3150/21-BEJ1335

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

Rights: Copyright © 2022 ISI/BS


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Vol.28 • No. 1 • February 2022
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