  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.
