Formula for the supremum distribution of a spectrally positive Lévy process

Abstract

In this article we derive formula for probability $\Prob(\sup_{t\leq T} (X(t)-ct)>u)$ where $X=\{X(t)\}$ is a spectrally positive Lévy process and $c\in\RL$. As an example we investigate the inverse Gaussian Lévy process.

Cited by in corpus (2)

• Lévy processes in storage and inventory problems
• Explicit formula for the supremum distribution of a spectrally negative stable process