  In this paper we characterize the distribution of the first exit time from an
arbitrary open set for a class of semi-Markov processes obtained as
time-changed Markov processes. We estimate the asymptotic behaviour of the
survival function (for large $t$) and of the distribution function (for small
$t$) and we provide some conditions for absolute continuity. We have been
inspired by a problem of neurophyshiology and our results are particularly
usefull in this field, precisely for the so-called Leacky Integrate-and-Fire
(LIF) models: the use of semi-Markov processes in these models appear to be
realistic under several aspects, e.g., it makes the intertimes between spikes a
r.v. with infinite expectation, which is a desiderable property. Hence, after
the theoretical part, we provide a LIF model based on semi-Markov processes.
