We consider the problem of estimating first exit distributions for one-dimensional diffusion processes. We provide analytic bounds and an approximation which is shown to be accurate in a range of numerical examples involving Brownian motion.
"The Hazard Rate Tangent Approximation for Boundary Hitting Times." Ann. Appl. Probab. 5 (2) 446 - 460, May, 1995. https://doi.org/10.1214/aoap/1177004773