Stability and mean-field limits of age dependent Hawkes processes
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Stability and mean-field limits of age dependent Hawkes processes. / Raad, Mads Bonde; Ditlevsen, Susanne; Löcherbach, Eva.
I: Annales de l'institut Henri Poincare (B) Probability and Statistics, Bind 56, Nr. 3, 2020, s. 1958-1990.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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