arXiv:2004.01887 Abstract | arXiv Analytics

arXiv:2004.01887 [math.PR]Abstract References Reviews Resources

Stability for Hawkes processes with inhibition

Published 2020-04-04Version 1

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.

Categories: math.PR

Subjects: 60G55, 60G57, 60J25, 60Fxx

Keywords: inhibition, multivariate non-linear hawkes process, hawkes system significantly affects, associated weight function matrix, populations acts excitatory

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