Matched transient and steady-state approximation of first-passage-time distributions of coloured noise driven leaky neurons

TL;DR

This paper introduces a novel method for approximating the first-passage-time distribution of leaky integrate-and-fire neurons driven by coloured noise, by matching transient and steady-state solutions of the membrane voltage distribution.

Contribution

It presents a new approximation technique leveraging eigen colouring of noise, extending to arbitrary coloured noise, and validated against numerical simulations.

Findings

The method accurately predicts first-passage-time distributions.

Approximations agree well with numerical simulations across parameters.

Extension to arbitrary coloured noise broadens applicability.

Abstract

The first-passage-time distribution of a leaky integrate-and-fire neuron driven by a characteristically coloured noise is approximated by matching a transient and a steady-state solution of the membrane voltage distribution. These approximations follow from a simple manipulation, made possible by the specific `eigen' colouring of the noise, which allows to express the membrane potential as a Gaussian diffusion process on top of a deterministic exponential movement. Following, the presented method is extended to the case of an arbitrarily coloured noise driving by factoring out the `eigen' noise and replacing the residue with an equivalent Gaussian process. It is shown that the obtained expressions agree well with numerical simulations for different values of the neuron parameters and noise colouring.