Stochastic integral and series representations for strictly stable distributions

Makoto Maejima; Jan Rosinski; Yohei Ueda

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arXiv · 1304.1580

Stochastic integral and series representations for strictly stable distributions

Makoto Maejima·Jan Rosinski·Yohei Ueda

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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.

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Makoto Maejima, Jan Rosinski, Yohei Ueda. 2013-09-17. Stochastic integral and series representations for strictly stable distributions. https://arxiv.org/abs/1304.1580

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