On First-Passage Problems for Asymmetric One-Dimensional Diffusions

摘要

For a, b ＞ 0, we consider a temporally homogeneous, one-dimensional diffusion process X(t) defined over I = (-b,a), with infinitesimal parameters depending on the sign of X(t). We suppose that, when X{t) reaches the position 0, it is reflected rightward to δ with probability p ＞ 0 and leftward to -δ with probability 1 - p, where δ ＞ 0. It is presented a method to find approximate formulae for the mean exit time from the interval (-b,a), and for the probability of exit through the right end a, generalizing the results of Lefebvre ([1]) holding, in the limit δ → 0, for asymmetric Brownian motion with drift.