  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.
