Stability and mean-field limits of age dependent Hawkes processes

Research output: Contribution to journal › Journal article › Research › peer-review

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Stability and mean-field limits of age dependent Hawkes processes. / Raad, Mads Bonde; Ditlevsen, Susanne; Löcherbach, Eva.

In: Annales de l'institut Henri Poincare (B) Probability and Statistics, Vol. 56, No. 3, 2020, p. 1958-1990.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Raad, MB, Ditlevsen, S & Löcherbach, E 2020, 'Stability and mean-field limits of age dependent Hawkes processes', Annales de l'institut Henri Poincare (B) Probability and Statistics, vol. 56, no. 3, pp. 1958-1990. https://doi.org/10.1214/19-AIHP1023

APA

Raad, M. B., Ditlevsen, S., & Löcherbach, E. (2020). Stability and mean-field limits of age dependent Hawkes processes. Annales de l'institut Henri Poincare (B) Probability and Statistics, 56(3), 1958-1990. https://doi.org/10.1214/19-AIHP1023

Vancouver

Raad MB, Ditlevsen S, Löcherbach E. Stability and mean-field limits of age dependent Hawkes processes. Annales de l'institut Henri Poincare (B) Probability and Statistics. 2020;56(3):1958-1990. https://doi.org/10.1214/19-AIHP1023

Author

Raad, Mads Bonde ; Ditlevsen, Susanne ; Löcherbach, Eva. / Stability and mean-field limits of age dependent Hawkes processes. In: Annales de l'institut Henri Poincare (B) Probability and Statistics. 2020 ; Vol. 56, No. 3. pp. 1958-1990.

Bibtex

@article{3c047108a2654e5da6d79263b9abcdb9,
title = "Stability and mean-field limits of age dependent Hawkes processes",
abstract = "In the last decade, Hawkes processes have received a lot of attention as good models for functional connectivity in neural spiking networks. In this paper we consider a variant of this process; the age dependent Hawkes process, which incorporates individual post-jump behavior into the framework of the usual Hawkes model. This allows to model recovery properties such as refractory periods, where the effects of the network are momentarily being suppressed or altered. We show how classical stability results for Hawkes processes can be improved by introducing age into the system. In particular, we neither need to a priori bound the intensities nor to impose any conditions on the Lipschitz constants. When the interactions between neurons are of mean-field type, we study large network limits and establish the propagation of chaos property of the system.",
keywords = "Age dependency, Coupling, Mean-field approximations, Multivariate nonlinear Hawkes processes, Multivariate point processes, Piecewise deterministic Markov processes, Stability",
author = "Raad, {Mads Bonde} and Susanne Ditlevsen and Eva L{\"o}cherbach",
year = "2020",
doi = "10.1214/19-AIHP1023",
language = "English",
volume = "56",
pages = "1958--1990",
journal = "Annales de l'Institut Henri Poincar{\'e}, Probabilit{\'e}s et Statistiques",
issn = "0246-0203",
publisher = "Institute Henri Poincar{\'e}",
number = "3",

}

RIS

TY - JOUR

T1 - Stability and mean-field limits of age dependent Hawkes processes

AU - Raad, Mads Bonde

AU - Ditlevsen, Susanne

AU - Löcherbach, Eva

PY - 2020

Y1 - 2020

N2 - In the last decade, Hawkes processes have received a lot of attention as good models for functional connectivity in neural spiking networks. In this paper we consider a variant of this process; the age dependent Hawkes process, which incorporates individual post-jump behavior into the framework of the usual Hawkes model. This allows to model recovery properties such as refractory periods, where the effects of the network are momentarily being suppressed or altered. We show how classical stability results for Hawkes processes can be improved by introducing age into the system. In particular, we neither need to a priori bound the intensities nor to impose any conditions on the Lipschitz constants. When the interactions between neurons are of mean-field type, we study large network limits and establish the propagation of chaos property of the system.

AB - In the last decade, Hawkes processes have received a lot of attention as good models for functional connectivity in neural spiking networks. In this paper we consider a variant of this process; the age dependent Hawkes process, which incorporates individual post-jump behavior into the framework of the usual Hawkes model. This allows to model recovery properties such as refractory periods, where the effects of the network are momentarily being suppressed or altered. We show how classical stability results for Hawkes processes can be improved by introducing age into the system. In particular, we neither need to a priori bound the intensities nor to impose any conditions on the Lipschitz constants. When the interactions between neurons are of mean-field type, we study large network limits and establish the propagation of chaos property of the system.

KW - Age dependency

KW - Coupling

KW - Mean-field approximations

KW - Multivariate nonlinear Hawkes processes

KW - Multivariate point processes

KW - Piecewise deterministic Markov processes

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=85091154277&partnerID=8YFLogxK

U2 - 10.1214/19-AIHP1023

DO - 10.1214/19-AIHP1023

M3 - Journal article

AN - SCOPUS:85091154277

VL - 56

SP - 1958

EP - 1990

JO - Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

JF - Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

SN - 0246-0203

IS - 3

ER -

ID: 249162354