Three upsilon transforms related to tempered stable distributions.(English)Zbl 1328.60042

Summary: 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 $$TS^q_\alpha$$.

MSC:

 60E07 Infinitely divisible distributions; stable distributions 60G51 Processes with independent increments; Lévy processes 60H05 Stochastic integrals
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