Formula for the supremum distribution of a spectrally positive Lévy process

preprint2012arXivOpen access

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.

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Formula for the supremum distribution of a spectrally positive Lévy process

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