A neuronal model with excitatory and inhibitory inputs governed by a birth-death process

Abstract

A stochastic model for the firing activity of a neuronal unit has been recently proposed in [4]. It includes the decay effect of the membrane potential in the absence of stimuli, and the occurrence of excitatory inputs driven by a Poisson process. In order to add the effects of inhibitory stimuli, we now propose a Stein-type model based on a suitable exponential transformation of a bilateral birth-death process on Z and characterized by state-dependent nonlinear birth and death rates. We perform an analysis of the probability distribution of the stochastic process describing the membrane potential and make use of a simulation-based approach to obtain some results on the firing density. © 2009 Springer-Verlag Berlin Heidelberg.