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2020 Stability for Hawkes processes with inhibition
Mads Bonde Raad, Eva Löcherbach
Electron. Commun. Probab. 25: 1-9 (2020). DOI: 10.1214/20-ECP312


We consider a multivariate non-linear Hawkes process in a multi-class setup where particles are organised within two populations of possibly different sizes, such that one of the populations acts excitatory on the system while the other population acts inhibitory on the system. The goal of this note is to present a class of Hawkes Processes with stable dynamics without assumptions on the spectral radius of the associated weight function matrix. This illustrates how inhibition in a Hawkes system significantly affects the stability properties of the system.


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Mads Bonde Raad. Eva Löcherbach. "Stability for Hawkes processes with inhibition." Electron. Commun. Probab. 25 1 - 9, 2020.


Received: 5 January 2020; Accepted: 5 April 2020; Published: 2020
First available in Project Euclid: 28 April 2020

zbMATH: 1439.60048
MathSciNet: MR4092763
Digital Object Identifier: 10.1214/20-ECP312

Primary: 60Fxx , 60G55 , 60G57 , 60J25

Keywords: Lyapunov functions , Multivariate nonlinear Hawkes processes , Piecewise deterministic Markov processes , stability


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