The law of the supremum of a stable Lévy process with no negative jumps

Violetta Bernyk, Robert C. Dalang, Goran Peskir

Let $X=(X_t{)}_{t\ge 0}$ be a stable Lévy 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 t…