Suprema of Lévy processes

Mateusz Kwaśnicki, Jacek Małecki, Michał Ryznar

In this paper we study the supremum functional $M_t={\sup }_{0\le s\le t}{X}_s$, where $X_t$, $t\ge 0$, is a one-dimensional Lévy process. Under very mild assumptions we provide a simple…