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December 2012 On a new class of tempered stable distributions: moments and regular variation
Michael Grabchak
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J. Appl. Probab. 49(4): 1015-1035 (December 2012). DOI: 10.1239/jap/1354716655

Abstract

We extend the class of tempered stable distributions, which were first introduced in Rosiński (2007). Our new class allows for more structure and more variety of the tail behaviors. We discuss various subclasses and the relations between them. To characterize the possible tails, we give detailed results about finiteness of various moments. We also give necessary and sufficient conditions for the tails to be regularly varying. This last part allows us to characterize the domain of attraction to which a particular tempered stable distribution belongs.

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Michael Grabchak. "On a new class of tempered stable distributions: moments and regular variation." J. Appl. Probab. 49 (4) 1015 - 1035, December 2012. https://doi.org/10.1239/jap/1354716655

Information

Published: December 2012
First available in Project Euclid: 5 December 2012

zbMATH: 1269.60018
MathSciNet: MR3058986
Digital Object Identifier: 10.1239/jap/1354716655

Subjects:
Primary: 60E07
Secondary: 60G51

Keywords: Infinite divisibility , regular variation , tail behavior , tempered stable distribution

Rights: Copyright © 2012 Applied Probability Trust

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Vol.49 • No. 4 • December 2012
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