  We present an approximate analytical expression for the escape rate of
time-dependent driven stochastic processes with an absorbing boundary such as
the driven leaky integrate-and-fire model for neural spiking. The novel
approximation is based on a discrete state Markovian modeling of the full
long-time dynamics with time-dependent rates. It is valid in a wide parameter
regime beyond the restraining limits of weak driving (linear response) and/or
weak noise. The scheme is carefully tested and yields excellent agreement with
three different numerical methods based on the Langevin equation, the
Fokker-Planck equation and an integral equation.
