On the instantaneous return process for neuronal diffusion models

The instantaneous return process is investigated for Wiener, Ornstein-Uhlenbeck and Feller neuronal models under the assumptions that after each firing the neuron's membrane potential is reset to a unique fixed value or that a preassigned uniform probability density characterizes the reset values. Steady-state probability densities and asymptotic moments are calculated and closed form expressions are obtained for asymptotic mean and variance of the neuronal membrane potential