We define a class of one dimensional diffusion processes whose transition p.d.f.'s satisfy some "strong" symmetry properties and a class of time-varying boundaries for which the first-passage-time and the transition pdf's with absorbing conditions on the boundaries can be obtained in closed form both for the cases of a single and of a pair of boundaries. Our findings are finally seen to include a result ingeniously obtained by Daniels for the standard Wiener process and a particular boundary.
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