Conditional propagation of chaos for mean field systems of interacting neurons

We study the stochastic system of interacting neurons introduced in [5] and [10] a diffusive scaling. The consists N neurons, each spiking randomly with rate depending on its membrane potential. At time, potential neuron is reset to 0 all other receive an additional amount which centred random variable order 1? N. In between successive spikes, neuron’s follows deterministic flow. prove convergence system, as N??, limit nonlinear jumping differential equation driven by Poisson measure Brownian motion W created central theorem. This underlying particle’s induces common noise factor for system. Conditionally W, different are independent conditional propagation chaos property. well-posedness adapting ideas [12] our frame. To distribution finite we introduce new martingale problem that well suited framework. uniqueness deduced from exchangeability