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2016 | OriginalPaper | Chapter

4. Heavy Tails

Author : Gennady Samorodnitsky

Published in: Stochastic Processes and Long Range Dependence

Publisher: Springer International Publishing

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Abstract

When we talk about the “tails” of a one-dimensional random variable X, we usually think about probabilities of the type P(X > x) and P(X < −x) for a large positive x, with the appropriate meaning of “right tail” and “left tail.” If \((X(t),\,t \in \mathbb{R})\) or \((X_{n},\,n \in \mathbb{Z})\) is a stationary stochastic process, the kind of marginal tails the process has may significantly impact the way memory expresses itself in the process. Particularly important is the distinction between stochastic processes with “light tails” and those with “heavy tails.”

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Title: Heavy Tails
Author: Gennady Samorodnitsky
Publisher: Springer International Publishing
Book: Stochastic Processes and Long Range Dependence
Print ISBN: 978-3-319-45574-7

Electronic ISBN: 978-3-319-45575-4

Copyright Year: 2016
DOI: https://doi.org/10.1007/978-3-319-45575-4_4