A Microscopic Spiking Neuronal Network for the Age-Structured Model

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 set of global activity variables with random delays. We show the well-posedness of the particle system and the mean-field equation. Moreover, by studying the tightness of the empirical measure, we prove the propagation of chaos property. Eventually, we quantify the rate of convergence by using the coupling method.