On the asymptotic behaviour of first passage times for diffusions - Keller, Gerhard; Kersting, Götz; Rösler, Uwe (Probability Theory and Related Fields, 1988)
We investigate the asymptotic behaviour of first passage times of diffusions or birth-death processes. Necessary and sufficient conditions in terms of moments and the speed and scale functions are given for convergence of the first passage times to a normal or an exponential distribution.