A state-dependent stochastic neuronal model with periodic inputs

A stochastic model for the firing activity of a neuronal unit has been recently proposed in Di Crescenzo and Martinucci (2007). It includes the decay effect of the membrane potential in the absence of stimuli, and the occurrence of time-varying excitatory inputs governed by a Poisson process. We perform an analysis of this model in the case of time-non-homogeneous excitatory stimuli arriving according to a periodic rate. The probability distribution of the membrane potential is given in a closed form. We also develop a simulation-based approach to study the firing density, together with the mean and the coefficient of variation of the firing times.