The Law of the Supremum of a Stable Lévy Process with No Negative Jumps

Let X=(X_t)_{t \ge 0} be a stable L\'evy process of index \alpha \in (1,2) with no negative jumps, and let S_t = \sup_{0 \le s \le t} X_s denote its running supremum for t>0. We show that the density function f_t of S_t can be characterized as the unique solution... Show more