Stochastic integral and series representations for strictly stable distributions

2013/04/04 by Makoto Maejima, Maejima, Makoto, Jan Rosinski +3
Mathematics · #60E07 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60E07

paper · pdf · doi:10.48550/arxiv.1304.1580

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

arxiv created 2013/09/17 · arxiv updated 2013/09/18

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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