A computational approach to first-passage-time problems for Gauss–Markov processes

A new computationally simple, speedy and accurate method is proposed to construct first-passage-time probability density functions for Gauss–Markov processes through time-dependent boundaries, both for fixed and for random initial states. Some applications to Brownian motion and to the Brownian bridge are then provided together with a comparison with some computational results by Durbin and by Daniels. Various closed-form results are also obtained for classes of boundaries that are intimately related to certain symmetries of the processes considered.