The distribution of the supremum for spectrally asymmetric Lévy processes

Zbigniew Michna, Zbigniew Palmowski, Martijn Pistorius

In this article we derive formulas for the probability $P({\sup }_{t\le T}X(t)>u)$ $T>0$ and $P({\sup }_{t<\infty }X(t)>u)$ where $X$ is a spectrally positive Lévy process with infinit…