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Pré-Publication, Document De Travail Année : 2015

A microscopic spiking neuronal network for the age-structured model

Résumé

We introduce a microscopic spiking network consistent with the age-structured/renewal equation proposed by Pakdaman, Perthame and Salort. It is a jump process interacting through a global activity variable with random delays. We show the well-posedness of the particle system and the mean-field equation. Moreover we show the propagation of chaos property and we quantify the rate of convergence under the assumption of exponential moments on the initial data.
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Dates et versions

hal-01121061 , version 1 (27-02-2015)
hal-01121061 , version 2 (20-05-2015)
hal-01121061 , version 3 (21-05-2015)

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Cristóbal Quiñinao. A microscopic spiking neuronal network for the age-structured model. 2015. ⟨hal-01121061v3⟩
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