Strong error bounds for the conditional propagation of chaos for mean field systems of neurons

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Seminar Données et Aléatoire Théorie & Applications

17/02/2022 - 14:00 Xavier Erny (X) Salle 106

We consider a mean field system of interacting neurons in a diffusive regime. The system consists of N neurons, each spiking randomly with rate depending on its membrane potential (each spike train is modeled by a point process). At its spiking time, the potential of the spiking neuron is reset to 0 and all other neurons receive an additional amount of potential which is a centred random variable of order N^{-1/2} (these random variables are the defined as marks of the point processes). In between successive spikes, each neuron's potential follows a deterministic flow. The convergence (as N goes to infinity) in distribution of these systems has already been proved, the subject of the talk is to establish a coupling between the system of N neurons and its limit with an L^1-control. A key ingredient in the proof is the approximation result of Komlos, Major and Tusnady, to couple the maked point processes of the N-neuron system with a Brownian motion created by a CLT-convergence in the limit system.