Mean-field limit of a stochastic particle system smoothly interacting through threshold hitting-times and applications to neural networks with dendritic component - Inria - Institut national de recherche en sciences et technologies du numérique
Journal Articles SIAM Journal on Mathematical Analysis Year : 2015

Mean-field limit of a stochastic particle system smoothly interacting through threshold hitting-times and applications to neural networks with dendritic component

Abstract

In this article we study the convergence of a stochastic particle system that interacts through threshold hitting times towards a novel equation of McKean-Vlasov type. The particle system is motivated by an original model for the behavior of a network of neurons, in which a classical noisy integrate-and-fire model is coupled with a cable equation to describe the dendritic structure of each neuron.
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Dates and versions

hal-01069398 , version 1 (29-09-2014)
hal-01069398 , version 2 (03-12-2014)
hal-01069398 , version 3 (06-01-2015)
hal-01069398 , version 4 (13-09-2015)

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Cite

James Inglis, Denis Talay. Mean-field limit of a stochastic particle system smoothly interacting through threshold hitting-times and applications to neural networks with dendritic component. SIAM Journal on Mathematical Analysis, 2015, 47 (5), pp.32. ⟨10.1137/140989042⟩. ⟨hal-01069398v4⟩
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