Stochastic Integral and Series Representations for Strictly Stable Distributions

Makoto Maejima (), Jan Rosiński () and Yohei Ueda ()
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Makoto Maejima: Keio University
Jan Rosiński: University of Tennessee
Yohei Ueda: Keio University

Journal of Theoretical Probability, 2015, vol. 28, issue 3, 989-1006

Abstract: 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 $$\alpha $$ α is greater than 1. We also give an explicit description of distributions possessing both representations.

Keywords: Strictly stable distribution; Stochastic integral representation; Series representation; 60E07 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10959-013-0518-8

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