English

Formula for the supremum distribution of a spectrally positive L\'evy process

Probability 2012-05-30 v6

Abstract

In this article we derive formula for probability \Prob(suptT(X(t)ct)>u)\Prob(\sup_{t\leq T} (X(t)-ct)>u) where X={X(t)}X=\{X(t)\} is a spectrally positive L\'evy process and c\RLc\in\RL. As an example we investigate the inverse Gaussian L\'evy process.

Keywords

Cite

@article{arxiv.1104.1976,
  title  = {Formula for the supremum distribution of a spectrally positive L\'evy process},
  author = {Zbigniew Michna},
  journal= {arXiv preprint arXiv:1104.1976},
  year   = {2012}
}