The tangent approximation to one-sided Brownian exit densities

SummaryLet p(t) be the density of the first-exit time of a Brownian motion over a one-sided moving boundary, and let p1(t) be the density at t of the first-exit time over the tangent to the boundary at t. When is p1(t) a good approximation to p(t)? We investigate this question by means of a new integral equation for p(t) which makes possible explicit estimates for the error of the approximation.