  Analytical expressions are put forward to investigate the forced spiking
activity of abstract neuron models such as the driven leaky integrate-and-fire
(LIF) model. The method is valid in a wide parameter regime beyond the
restraining limits of weak driving (linear response) and/or weak noise. The
novel approximation is based on a discrete state Markovian modeling of the full
dynamics with time-dependent rates. The scheme yields very good agreement with
numerical Langevin and Fokker-Planck simulations of the full non-stationary
dynamics for both, the first-passage time statistics and the interspike
interval (residence time) distributions.
