Self-similar processes are stochastic processes that are
invariant in distribution under suitable time scaling, and are a
subject intensively studied in the last few decades. This book
presents the basic properties of these processes and focuses on the
study of their variation using stochastic analysis. While
self-similar processes, and especially fractional Brownian motion,
have been discussed in several books, some new classes have
recently emerged in the scientific literature. Some of them are
extensions of fractional Brownian motion (bifractional Brownian
motion, subtractional Brownian motion, Hermite processes), while
others are solutions to the partial differential equations driven
by fractional noises.
In this monograph the author discusses the basic properties of
these new classes of self-similar processes and their
interrelationship. At the same time a new approach (based on
stochastic calculus, especially Malliavin calculus) to studying the
behavior of the variations of self-similar processes has been
developed over the last decade. This work surveys these recent
techniques and findings on limit theorems and Malliavin calculus.
"
General
Imprint: |
Springer International Publishing AG
|
Country of origin: |
Switzerland |
Series: |
Probability and Its Applications |
Release date: |
August 2013 |
First published: |
2013 |
Authors: |
Ciprian Tudor
|
Dimensions: |
235 x 155 x 17mm (L x W x T) |
Format: |
Hardcover
|
Pages: |
268 |
Edition: |
2013 ed. |
ISBN-13: |
978-3-319-00935-3 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Applied mathematics >
Stochastics
|
LSN: |
3-319-00935-4 |
Barcode: |
9783319009353 |
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