Three Upsilon Transforms Related to Tempered Stable Distributions

Abstract

We discuss the properties of three upsilon transforms, which are related to the class of $p$-tempered $\alpha$-stable ($T{S}_{\alpha }^p$) 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 $T{S}_{\beta }^p$ distributions into those of $T{S}_{\alpha }^q$.

References in corpus (2)

• Transformations of infinitely divisible distributions via improper stochastic integrals
• Inversions of Levy Measures and the Relation Between Long and Short Time Behavior of Levy Processes