Mean-field analysis of an excitatory neuronal network: application to systemic risk modeling? | Vidéo | Carmin.tv

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Mean-field analysis of an excitatory neuronal network: application to systemic risk modeling?

De François Delarue

Apparaît dans la collection : Advances in stochastic analysis for risk modeling / Analyse stochastique pour la modélisation des risques

Inspired by modeling in neurosciences, we here discuss the well-posedness of a networked integrate-and-fire model describing an infinite population of companies which interact with one another through their common statistical distribution. The interaction is of the self-excitatory type as, at any time, the debt of a company increases when some of the others default: precisely, the loss it receives is proportional to the instantaneous proportion of companies that default at the same time. From a mathematical point of view, the coefficient of proportionality, denoted by a, is of great importance as the resulting system is known to blow-up when a takes large values, a blow-up meaning that a macroscopic proportion of companies may default at the same time. In the current talk, we focus on the complementary regime and prove that existence and uniqueness hold in arbitrary time without any blow-up when the excitatory parameter is small enough.

Informations sur la vidéo

Date de captation 09/09/2014
Date de publication 11/09/2014
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.18560203
Citer cette vidéo DELARUE, François (09/09/2014). Mean-field analysis of an excitatory neuronal network: application to systemic risk modeling?. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18560203
URL https://dx.doi.org/10.24350/CIRM.V.18560203

Domaine(s)

Bibliographie

M. J. Cáceres, J. A. Carrillo, and B. Perthame, Analysis of nonlinear noisy integrate & fire neuron models: blow-up and steady states, J. Math. Neurosci., 1 (2011), p. 7 - http://dx.doi.org/10.1186/2190-8567-1-7
F. Delarue, J. Inglis, S. Rubenthaler, and E. Tanré, Global solvability of a networked integrate-and-fire model of McKean-Vlasov type. arxiv:1211.0299v4, 2014 - http://arxiv.org/abs/1211.0299v4
F. Delarue, J. Inglis, S. Rubenthaler, and E. Tanré, Particle systems with a singular mean-field self-excitation. Application to neuronal networks. arxiv:1406.1151, 2014 - http://arxiv.org/abs/1406.1151v2

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