Weak noise approximation for the Kolmogorov forward equation for a leaky integrate-and-fire neuron subject to stochastic stimulation

Abstract

We develop a weak noise approximation for the Kolmogorov forward equation governing the dynamics of a leaky integrate-and-fire neuron subject to white noise. Although being very simple, our approximation provides accurate results as far the magnitude of noise-induced fluctuations $\Delta$ remains much smaller than the distance $A$ between the mean potential (center of mass) and the excitation threshold. The error for the firing rate is $<3\text{\%}$ if $A/\Delta >3$ for the stationary stimuli and if $A/\Delta >5$ for time-varying stimuli.