  We consider a bivariate diffusion process and we study the first passage time
of one component through a boundary. We prove that its probability density is
the unique solution of a new integral equation and we propose a numerical
algorithm for its solution. Convergence properties of this algorithm are
discussed and the method is applied to the study of the integrated Brownian
Motion and to the integrated Ornstein Uhlenbeck process. Finally a model of
neuroscience interest is also discussed.
