A note on the supremum of a stable process

R. A. Doney

If $X$ is a spectrally positive stable process of index $\alpha \in (1,2)$ whose Lévy measure has density $c{x}^{-\alpha -1}$ on $(0,\infty ),$ and $S_1={\sup }_{0<t\le 1}{X}_t,$ it is known that $P(S_…