Effect of the Synaptic Time Constant on Stochastic Spiking Neurons

In this article, we theoretically examine the responses of spiking neurons to spike sequences which obey an inhomogeneous Poisson process. When statistically independent random inputs are provided, the probability densities of membrane potential converge to a Gaussian distribution. In this case, the stochastic process of the membrane potential becomes a Gauss process. We find that frequently used spike response functions become multiple-Markov Gauss processes. We introduce a calculation method precisely obtain the dynamics of the membrane potential and the firing probability. The preciseness of our theory is confirmed by comparing with the Monte-Calro simulations. We also find that the synaptic time constant of the spike response function which is ignored in many stochastic process studies has significant influence on firing probability.