The modeling of stochastic dependence is fundamental for
understanding random systems evolving in time. When measured
through linear correlation, many of these systems exhibit a slow
correlation decay--a phenomenon often referred to as long-memory or
long-range dependence. An example of this is the absolute returns
of equity data in finance. Selfsimilar stochastic processes
(particularly fractional Brownian motion) have long been postulated
as a means to model this behavior, and the concept of
selfsimilarity for a stochastic process is now proving to be
extraordinarily useful. Selfsimilarity translates into the equality
in distribution between the process under a linear time change and
the same process properly scaled in space, a simple scaling
property that yields a remarkably rich theory with far-flung
applications.
After a short historical overview, this book describes the
current state of knowledge about selfsimilar processes and their
applications. Concepts, definitions and basic properties are
emphasized, giving the reader a road map of the realm of
selfsimilarity that allows for further exploration. Such topics as
noncentral limit theory, long-range dependence, and operator
selfsimilarity are covered alongside statistical estimation,
simulation, sample path properties, and stochastic differential
equations driven by selfsimilar processes. Numerous references
point the reader to current applications.
Though the text uses the mathematical language of the theory of
stochastic processes, researchers and end-users from such diverse
fields as mathematics, physics, biology, telecommunications,
finance, econometrics, and environmental science will find it an
ideal entry point for studying the already extensive theory and
applications of selfsimilarity.
General
Imprint: |
Princeton University Press
|
Country of origin: |
United States |
Series: |
Princeton Series in Applied Mathematics |
Release date: |
August 2002 |
First published: |
August 2002 |
Authors: |
Paul Embrechts
|
Dimensions: |
235 x 152 x 15mm (L x W x T) |
Format: |
Hardcover - Trade binding
|
Pages: |
128 |
ISBN-13: |
978-0-691-09627-8 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Applied mathematics >
Stochastics
|
LSN: |
0-691-09627-9 |
Barcode: |
9780691096278 |
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