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Tempered Stable Distributions

Stochastic Models for Multiscale Processes

  • Book
  • © 2016

Overview

Authors:
  1. Michael Grabchak

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

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  • Provides a thorough survey of tempered stable distributions and their associate Levy processes
  • Self-contained discussion and overview makes it perfect for researchers interested in learning about tempered stable distributions
  • Many new cutting-edge results of interest to specialists in the area

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

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Introduction

    • Michael Grabchak
    Pages 1-4

  3. Preliminaries

    • Michael Grabchak
    Pages 5-13

  4. Tempered Stable Distributions

    • Michael Grabchak
    Pages 15-45

  5. Limit Theorems for Tempered Stable Distributions

    • Michael Grabchak
    Pages 47-66

  6. Multiscale Properties of Tempered Stable Lévy Processes

    • Michael Grabchak
    Pages 67-82

  7. Parametric Classes

    • Michael Grabchak
    Pages 83-95

  8. Applications

    • Michael Grabchak
    Pages 97-109

  9. Epilogue

    • Michael Grabchak
    Pages 111-112

  10. Back Matter

    Pages 113-118
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Keywords

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.

Reviews

“This is a very nicely written book on tempered stable distributions. The exposition is careful and very readable. … The book will be a very helpful source for researchers working in the area of tempered stable distributions and for all that want to apply them.” (Alexander Lindner, zbMATH 1361.60003, 2017)

Authors and Affiliations

  • Dept of Mathematics and Statistics, University of North Carolina, Charlotte, USA

    Michael Grabchak

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