Towards the modeling of neuronal firing by Gaussian processes

This paper focuses on the outline of some computational methods for the approximate solution of the integral equations for the neuronal fring probability density and an algorithm for the generation of sample-paths in order to construct histograms estimating the fring densities. Our results originate from the study of non-Markov stationary Gaussian neuronal models with the aim to determine the neuron's fring probability density function. A parallel algorithm has been implemented in order to simulate large numbers of sample paths of Gaussian processes character- ized by damped oscillatory covariances in the presence of time dependent boundaries. The analysis based on the simulation procedure provides an alternative research tool when closed-form results or analytic evaluation of the neuronal fring densities are not available.