Tempered Stable Distributions Stochastic Models for Multiscale Processes

Tempered Stable Distributions: Stochastic Models for Multiscale Processes
Springer | Mathematics | February 27, 2016 | ISBN-10: 3319249258 | 118 pages | pdf | 1.39 mb

Authors: Grabchak, Michael
​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

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.

Topics
Probability Theory and Stochastic Processes
Quantitative Finance

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Title: Tempered Stable Distributions Stochastic Models for Multiscale Processes
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