We calculate crossing probabilities and one-sided last exit time densities
for a class of moving barriers on an interval [0,T] via Schwartz
distributions. We derive crossing probabilities and first hitting time
densities for another class of barriers on [0,T] by proving a Schwartz
distribution version of the method of images. Analytic expressions for crossing
probabilities and related densities are given for new explicit and
semi-explicit barriers.Comment: Published in at http://dx.doi.org/10.1214/07-AAP488 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
