Computational Methods for the Evaluation of Neuron's Firing Densities

Some analytical and computational methods are outlined, that are suitable to determine the upcrossing first passage time probability density for some Gauss-Markov processes that have been used to model the time course of neurons membrane potential. In such a framework, the neuronal firing probability density is identified with that of the first passage time upcrossing of the considered process through a preassigned threshold function. In order to obtain reliable evaluations of these densities, ad hoc numerical and simulation algorithms are implemented.