English

Stochastic integral and series representations for strictly stable distributions

Probability 2013-09-18 v2

Abstract

In this paper we find and develop a stochastic integral representation for the class of strictly stable distributions. We establish an explicit relationship between stochastic integral and shot-noise series representations of strictly stable distributions, which shows that the class of distributions representable by stochastic integral is larger than the class representable by a shot-noise series. This inclusion is proper when the stability index is greater than 1. We also give an explicit description of distributions possessing both representations.

Keywords

Cite

@article{arxiv.1304.1580,
  title  = {Stochastic integral and series representations for strictly stable distributions},
  author = {Makoto Maejima and Jan Rosinski and Yohei Ueda},
  journal= {arXiv preprint arXiv:1304.1580},
  year   = {2013}
}

Comments

To appear in Journal of Theoretical Probability; updated title, exposition improved; 18 pages

R2 v1 2026-06-21T23:54:18.799Z