Some exact formulas for threshold neuron models: correlations and synchrony

In this paper we study some threshold neuron models with focus on speci c features as correlations and synchrony input of spikes. These models have received much attention recently in neuroscience research. Our aim is in particular to provide exact formulas for these threshold neuron models in order to investigate more deeply the statistical theory behind these stochastic models. Furthermore we prove a bivariate Central Limit Theorem for a two-neurons model for an in nite horizon time, using a coupled harmonic oscillators. We also present simulated examples which illustrate our theoretical results.