On the evaluation of first-passage-time densities for diffusion processes

Use of a Volterra second-kind integral equation is made to evaluate first passage time probability density functions through time varying boundaries for diffusion processes. The solutions are constructed in the form of infinite series whose terms are expressed as multidimensional integrals. An evaluation of such solutions is provided for the cases of Wiener and Ornstein-Uhlenbeck processes by standard numerical procedures, and by a Monte Carlo method. Results are discussed with reference to other existing computational methods.