  We consider the statistics of occupation times, the number of visits at the
origin and the survival probability for a wide class of stochastic processes,
which can be classified as renewal processes. We show that the distribution of
these observables can be characterized by a single parameter, that is connected
to a local property of the probability density function (PDF) of the process,
viz., the probability of occupying the origin at time $t$, $P(t)$. We test our
results for two different models of lattice random walks with spatially
inhomogeneous transition probabilities, one of which of non-Markovian nature,
and find good agreement with theory. We also show that the distributions depend
only on the occupation probability of the origin by comparing them for the two
systems: when $P(t)$ show the same long-time behavior, each observable follows
indeed the same distribution.
