A first passage problem for a bivariate diffusion process: numerical   solution with an application to neuroscience
  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. 
Elisa Benedetto, Laura Sacerdote and Cristina Zucca
math.PR q-bio.NC