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 Δ 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 for the stationary stimuli and if A/Δ>5 for time-varying stimuli.

Keywords

• Forward Kolmogorov equation
• Leaky integrate-and-fire neuron
• Self-similar solution
• Neural mass models