A First-Passage Problem for Exponential Integrated Diffusion Processes
Mario Lefebvre · Journal of Stochastic Analysis · 2022
Let d Y (t) = Z(t) dt, where Z(t) is a one-dimensional diffusion process, and X(t) = X(0) e Y (t)-Y (0) .We denote by T (x, z) the first time the two-dimensional process (X(t), Z(t)) leaves a rectangle located in the first quadrant.The problem of computing the moment-generating function M and the mean m of T (x, z) is considered.Explicit results are obtained in important particular cases for the Laplace transform of M and of m.A generalization is also presented.