  Variability in neural responses is an ubiquitous phenomenon in neurons,
usually modeled with stochastic differential equations. In particular,
stochastic integrate-and-fire models are widely used to simplify theoretical
studies. The statistical properties of the generated spikes depend on the
stimulating input current. Given that real sensory neurons are driven by
time-dependent signals, here we study how the inter-spike interval distribution
of integrate-and-fire neurons depends on the evolution of the stimulus, in a
quasi-static limit. We obtain a closed-form expression for this distribution,
and we compare it to the one obtained with numerical simulations for several
time-dependent currents. For slow inputs, the quasi-static distribution
provides a very good description of the data. The results obtained for the
integrate-and-fire model can be extended to other non-autonomous stochastic
systems where the first passage time problem has an explicit solution.
