English

Fonctions de Mittag-Leffler et processus de L\'evy stables sans saut n\'egatif

Probability 2009-04-16 v1

Abstract

It is noticed that a certain transform of the Mittag-Leffler function Ea is completely monotone for a in [1,2]. Using the explicit expressions of its Bernstein density, an identity in law between suprema of completely asymmetric Levy a-stable processes. In the spectrally positive case, we retrieve the exact expression of a unilateral small deviation constant which had been previously obtained by a different method by Bernyk, Dalang and Peskir.

Keywords

Cite

@article{arxiv.0904.2191,
  title  = {Fonctions de Mittag-Leffler et processus de L\'evy stables sans saut n\'egatif},
  author = {Thomas Simon},
  journal= {arXiv preprint arXiv:0904.2191},
  year   = {2009}
}