  We study the distribution of the time to explosion for one-dimensional
diffusions. We relate this question to computing the expectations of suitable
nonnegative local martingales, and to the distributions of related diffusions
with unit variance. Moreover, we characterize the distribution function of the
time to explosion as the minimal solution to a certain Cauchy problem for an
appropriate parabolic differential equation; this leads to alternative
characterizations of Feller's criterion for explosions. We discuss in detail
several examples for which it is possible to obtain analytic expressions for
the corresponding distribution of the time to explosion, using the
methodologies developed in the paper.
