Open Access
2015 Three upsilon transforms related to tempered stable distributions
Michael Grabchak
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Electron. Commun. Probab. 20: 1-10 (2015). DOI: 10.1214/ECP.v20-4366


We discuss the properties of three upsilon transforms, which are related to the class of $p$-tempered $\alpha$-stable ($TS^p_\alpha$) distributions. In particular, we characterize their domains and show how they can be represented as compositions of each other. Further, we show that if $-\infty<\beta<\alpha<2$ and $0<q<p<\infty$ then they can be used to transform the Lévy measures of $TS^p_\beta$ distributions into those of $TS^q_\alpha$.


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Michael Grabchak. "Three upsilon transforms related to tempered stable distributions." Electron. Commun. Probab. 20 1 - 10, 2015.


Accepted: 6 November 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1328.60042
MathSciNet: MR3434199
Digital Object Identifier: 10.1214/ECP.v20-4366

Primary: 60E07
Secondary: 60G51 , 60H05

Keywords: tempered stable distributions , transforms of Lévy measures , upsilon transforms

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