A first passage problem for a bivariate diffusion process: Numerical solution with an application to neuroscience when the process is Gauss-Markov

摘要

We consider a bivariate Gauss-Markov process and we study the first passage time of one component through a constant boundary. We prove that its probability density function 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 discussed.