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Tempered Stable Distributions

Part of the book series: SpringerBriefs in Mathematics ((BRIEFSMATH))

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Abstract

This chapter contains a brief discussion of the motivation for introducing the class of tempered stable distributions.

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Notes

  1. 1.

    Lévy flights are random walks, where the step sizes are independent and identically distributed draws from an infinite variance α-stable distribution, see [52]. The term “truncated Lévy flight” was also originally used to refer to a random walk, but has now come to refer to the underlying distribution.

  2. 2.

    This is because infinitely divisible distributions cannot have a bounded support, see Theorem 24.3 in [69].

  3. 3.

    Background on infinitely divisible distributions and Lévy measures is given in Section 2.2

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of North Carolina, Charlotte, NC, USA

    Michael Grabchak

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  1. Michael Grabchak
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© 2016 Michael Grabchak

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Grabchak, M. (2016). Introduction. In: Tempered Stable Distributions. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-24927-8_1

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