English

Hitting densities for spectrally positive stable processes

Probability 2010-02-09 v1

Abstract

A multiplicative identity in law connecting the hitting times of completely asymmetric α\alpha-stable L\'evy processes in duality is established. In the spectrally positive case, this identity allows with an elementary argument to compute fractional moments and to get series representations for the density. We also prove that the hitting times are unimodal as soon as α3/2.\alpha\le 3/2. Analogous results are obtained, in a much simplified manner, for the first passage time across a positive level.

Keywords

Cite

@article{arxiv.1002.1540,
  title  = {Hitting densities for spectrally positive stable processes},
  author = {Thomas Simon},
  journal= {arXiv preprint arXiv:1002.1540},
  year   = {2010}
}
R2 v1 2026-06-21T14:44:26.683Z