Gaussian process approach to stochastic spiking neurons with reset

Abstract

This article theoretically examines the behavior of spiking neurons whose input spikes obey an inhomogeneous Poisson process. Since the probability density of the membrane potential converges to a Gaussian distribution, the stochastic process becomes a Gaussian process.With a frequently-used spike response function, the process becomes a multiple-Markov Gaussian process. We develop a method which can precisely calculate the dynamics of the membrane potential and the firing probability. The effect of reset after firing is also considered. We find that the synaptic time constant of the spike response function, which has often been ignored in existing stochastic process studies, has significant influence on the firing probability.