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?

By François Delarue

Appears in 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.

Information about the video

Date of recording 09/09/2014
Date of publication 11/09/2014
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.18560203
Cite this video 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

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Bibliography

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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