A first passage problem for three-dimensional diffusion processes

Abstract

Let d(t) = [Φ(y(t)) + Ψ(z(t))]dt, where y(t) and z(t) are independent diffusion process. The problem of computing the moment generating function and the moments of[T(y, z)], where T(y, z) is a first passage time for (y(t), z(t)), is considered and solved explicitly in particular instances.