On the First Exit Time of a Completely Asymmetric Stable Process from a Finite Interval

We compute the Laplace transform of the distribution of the first exit time from a finite interval for a completely asymmetric stable process. The formula involves a Mittag-Leffler function and its derivative. As an application, we determine the asymptotic tail behaviour of the foregoing distribution, and deduce an extension of the law of the iterated logarithm of Chung.