First Passage Time For Multidimensional Diffusion Processes

This paper consider the first passage time problem of multidimensional diffusion processes. First, we consider the problem of a bivariate diffusion processes under time dependent boundary. We propose the numerical algorithm of the problem via turning the upper limit of integral of the Volterra-Fredholm equation into function. Second, with the help of matlab, we implement this algorithm and get the numerical solution of the bivariate Winer processes under special linear boundary. Third, we consider the FPT problem of three-dimensional diffusion processes under constant absorbing boundary. Via extending the Volterra-Fredholm equation into three-dimension and Euler algorithm, we obtain the numerical algorithm of the problem.