Stability for hawkes processes with inhibition

Mads Bonde Raad; Eva Löcherbach

doi:10.1214/20-ECP312

Stability for hawkes processes with inhibition

Mads Bonde Raad
, Eva Löcherbach

Department of Mathematical Sciences
University of Copenhagen
Université Paris 1 Panthéon-Sorbonne

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

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.

Original language	English
Article number	33
Pages (from-to)	1-9
Number of pages	9
Journal	Electronic Communications in Probability
Volume	25
DOIs	https://doi.org/10.1214/20-ECP312
Publication status	Published - 1 Jan 2020
Externally published	Yes

Keywords

Lyapunov functions
Multivariate nonlinear Hawkes processes
Piecewise deterministic Markov processes
Stability

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10.1214/20-ECP312

Cite this

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AB - 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.

KW - Lyapunov functions

KW - Multivariate nonlinear Hawkes processes

KW - Piecewise deterministic Markov processes

KW - Stability

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JF - Electronic Communications in Probability

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ER -

Stability for hawkes processes with inhibition

Abstract

Keywords

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