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The first-passage-time distribution of a leaky integrate-and-fire neurondriven by a characteristically coloured noise is approximated by matching atransient and a steady-state solution of the membrane voltage distribution.These approximations follow from a simple manipulation, made possible by thespecific `eigen' colouring of the noise, which allows to express the membranepotential as a Gaussian diffusion process on top of a deterministic exponentialmovement. Following, the presented method is extended to the case of anarbitrarily coloured noise driving by factoring out the `eigen' noise andreplacing the residue with an equivalent Gaussian process. It is shown that theobtained expressions agree well with numerical simulations for different valuesof the neuron parameters and noise colouring.

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