  We consider a random walk in confined geometry, starting from a site and
eventually reaching a target site. We calculate analytically the distribution
of the occupation time on a third site, before reaching the target site. The
obtained distribution is exact, and completely explicit in the case or
parallepipedic confining domains. We discuss implications of these results in
two different fields: The mean first passage time for the random trap model is
computed in dimensions greater than 1, and is shown to display a non-trivial
dependence with the source and target positions ; The probability of reaction
with a given imperfect center before being trapped by another one is also
explicitly calculated, revealing a complex dependence both in geometrical and
chemical parameters.
