Stability for Hawkes processes with inhibition

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Standard

Stability for Hawkes processes with inhibition. / Raad, Mads Bonde; Locherbach, Eva.

I: Electronic Communications in Probability, Bind 25, 33, 2020, s. 1-9.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Raad, MB & Locherbach, E 2020, 'Stability for Hawkes processes with inhibition', Electronic Communications in Probability, bind 25, 33, s. 1-9. https://doi.org/10.1214/20-ECP312

APA

Raad, M. B., & Locherbach, E. (2020). Stability for Hawkes processes with inhibition. Electronic Communications in Probability, 25, 1-9. [33]. https://doi.org/10.1214/20-ECP312

Vancouver

Raad MB, Locherbach E. Stability for Hawkes processes with inhibition. Electronic Communications in Probability. 2020;25:1-9. 33. https://doi.org/10.1214/20-ECP312

Author

Raad, Mads Bonde ; Locherbach, Eva. / Stability for Hawkes processes with inhibition. I: Electronic Communications in Probability. 2020 ; Bind 25. s. 1-9.

Bibtex

@article{1861eebe5dd1433c8d67ff1811f09541,
title = "Stability for Hawkes processes with inhibition",
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.",
keywords = "multivariate nonlinear Hawkes processes, stability, piecewise deterministic Markov processes, Lyapunov functions",
author = "Raad, {Mads Bonde} and Eva Locherbach",
year = "2020",
doi = "10.1214/20-ECP312",
language = "English",
volume = "25",
pages = "1--9",
journal = "Electronic Communications in Probability",
issn = "1083-589X",
publisher = "Institute of Mathematical Statistics",

}

RIS

TY - JOUR

T1 - Stability for Hawkes processes with inhibition

AU - Raad, Mads Bonde

AU - Locherbach, Eva

PY - 2020

Y1 - 2020

N2 - 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.

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 - multivariate nonlinear Hawkes processes

KW - stability

KW - piecewise deterministic Markov processes

KW - Lyapunov functions

U2 - 10.1214/20-ECP312

DO - 10.1214/20-ECP312

M3 - Journal article

VL - 25

SP - 1

EP - 9

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

SN - 1083-589X

M1 - 33

ER -

ID: 242416961