Tempered Stable Distributions

Stochastic Models for Multiscale Processes

  • Michael Grabchak

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Michael Grabchak
    Pages 1-4
  3. Michael Grabchak
    Pages 5-13
  4. Michael Grabchak
    Pages 15-45
  5. Michael Grabchak
    Pages 83-95
  6. Michael Grabchak
    Pages 97-109
  7. Michael Grabchak
    Pages 111-112
  8. Back Matter
    Pages 113-118

About this book


This brief is concerned with tempered stable distributions and their associated Levy processes. It is a good text for researchers interested in learning about tempered stable distributions. 

A tempered stable distribution is one which takes a stable distribution and modifies its tails to make them lighter. The motivation for this class comes from the fact that infinite variance stable distributions appear to provide a good fit to data in a variety of situations, but the extremely heavy tails of these models are not realistic for most real world applications. The idea of using distributions that modify the tails of stable models to make them lighter seems to have originated in the influential paper of Mantegna and Stanley (1994). Since then, these distributions have been extended and generalized in a variety of ways. They have been applied to a wide variety of areas including mathematical finance, biostatistics,computer science, and physics.


Infinitely Divisible Distributions Levy Processes Stable Distributions Tempered Heavy Tails Tempered Stable Distributions Weak Convergence

Authors and affiliations

  • Michael Grabchak
    • 1
  1. 1.Dept of Mathematics and StatisticsUniversity of North CarolinaCharlotteUSA

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