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On a new Class of Tempered Stable Distributions: Moments and Regular Variation

Part of: Distribution theory - Probability Stochastic processes

Published online by Cambridge University Press:  30 January 2018

Michael Grabchak
Michael Grabchak*
Affiliation:
University of North Carolina at Charlotte
*
∗ Postal address: University of North Carolina at Charlotte, 376 Fretwell Hall, 9201 University City Blvd, Charlotte, NC 28223, USA. Email address: mgrabcha@uncc.edu
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Abstract

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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.

Keywords

Infinite divisibilitytempered stable distributionregular variationtail behavior

MSC classification

Primary: 60E07: Infinitely divisible distributions; stable distributions
Secondary: 60G51: Processes with independent increments; L'evy processes
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 4 , December 2012 , pp. 1015 - 1035
Copyright
© Applied Probability Trust 

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