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 global activity variable 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 under the assumption of compactly supported initial data.