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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 we show the propagation of chaos property and we quantify the rate of convergence under the assumption of exponential moments on the initial data.

preprint2015arXivOpen access
Cristóbal Quiñinao
math.AP
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Open access1 author1 topic
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Cristóbal Quiñinao

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