For one-dimensional Brownian motion, the first hitting time of a point has infinite mean while the exit time from an interval has finite exponential moments. In this note we establish its counterparts for symmetric stable processes. The Laplace transform of the first hitting time of the integer...

We consider a one-dimensional random walk which is conditioned to stay non-negative and is "weakly pinned" to zero. This model is known to exhibit a phase transition as the strength of the weak pinning varies. We prove path space limit theorems which describe the macroscopic shape of the path...