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Multiscale analysis of complex time series : integration of chaos and random fractal theory, and beyond
- Available as
- Online
- Physical
- Summary
-
"Chaos and random fractal theory are two of the most important theories developed for data analysis. Until now, there has been no single book that encompasses all of the basic concepts necessary fo...
"Chaos and random fractal theory are two of the most important theories developed for data analysis. Until now, there has been no single book that encompasses all of the basic concepts necessary for researchers to fully understand the ever-expanding literature and apply novel methods to effectively solve their signal processing problems. Multiscale Analysis of Complex Time Series fills this pressing need by presenting chaos and random fractal theory in a unified manner."--Jacket.
Details
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- Creator
- Jianbo Gao [and others]
- Format
- Books
- Language
- English
- Contributors
- Publication
-
- Hoboken, N.J. : Wiley-Interscience, [2007]
- ©2007
- Physical Details
-
- 1 online resource (xiv, 352 pages) : illustrations
- ISBNs
- 0470191651, 0470191643, 9781280974465, 9780470191651, 9780470191644, 9780471654704, 128097446X, 9786610974467, 0471654701
- OCLC
- ocn181350120, ocn124165140
- Includes bibliographical references (pages 319-346) and index.
- Cover -- COVER -- TOC36;CONTENTS -- Preface -- CH36;1 Introduction -- 146;1 Examples of multiscale phenomena -- 146;2 Examples of challenging problems to be pursued -- 146;3 Outline of the book -- 146;4 Bibliographic notes -- CH36;2 Overview of fractal and chaos theories -- 246;1 Prelude to fractal geometry -- 246;2 Prelude to chaos theory -- 246;3 Bibliographic notes -- 246;4 Warmup exercises -- CH36;3 Basics of probability theory and stochastic processes -- 346;1 Basic elements of probability theory -- 346;2 Commonly used distributions -- 346;3 Stochastic processes -- 346;4 Special topic58; How to find relevant information for a new field quickly -- 346;5 Bibliographic notes -- 346;6 Exercises -- CH36;4 Fourier analysis and wavelet multiresolution analysis -- 446;1 Fourier analysis -- 446;2 Wavelet multiresolution analysis -- 446;3 Bibliographic notes -- 446;4 Exercises -- CH36;5 Basics of fractal geometry -- 546;1 The notion of dimension -- 546;2 Geometrical fractals -- 546;3 Power law and perception of self45;similarity -- 546;4 Bibliographic notes -- 546;5 Exercises -- CH36;6 Self45;similar stochastic processes -- 646;1 General definition -- 646;2 Brownian motion 40;Bm41; -- 646;3 Fractional Brownian motion 40;fBm41; -- 646;4 Dimensions of Bm and fBm processes -- 646;5 Wavelet representation of fBm processes -- 646;6 Synthesis of fBm processes -- 646;7 Applications -- 646;8 Bibliographic notes -- 646;9 Exercises -- CH36;7 Stable laws and Levy motions -- 746;1 Stable distributions -- 746;2 Summation of strictly stable random variables -- 746;3 Tail probabilities and extreme events -- 746;4 Generalized central limit theorem -- 746;5 Levy motions -- 746;6 Simulation of stable random variables -- 746;7 Bibliographic notes -- 746;8 Exercises -- CH36;8 Long memory processes and structure45;function45;based multifractal analysis -- 846;1 Long memory58; basic definitions -- 846;2 Estimation of the Hurst parameter -- 846;3 Random walk representation and structure45;function8211;based multifractal analysis -- 846;4 Other random walk45;based scaling parameter estimation -- 846;5 Other formulations of multifractal analysis -- 846;6 The notion of finite scaling and consistency of H estimators -- 846;7 Correlation structure of ON47;OFF intermittency and Levy motions -- 846;8 Dimension reduction of fractal processes using principal component analysis -- 846;9 Broad applications -- 846;10 Bibliographic notes -- 846;11 Exercises -- CH36;9 Multiplicative multifractals -- 946;1 Definition -- 946;2 Construction of multiplicative multifractals -- 946;3 Properties of multiplicative multifractals -- 946;4 Intermittency in fully developed turbulence -- 946;5 Applications -- 946;6 Bibliographic notes -- 946;7 Exercises -- CH36;10 Stage45;dependent multiplicative processes -- 1046;1 Description of the model -- 1046;2 Cascade representation of 147;fb processes -- 1046;3 Application58; Modeling heterogeneous Internet traffic -- 1046;4 Bibliographic notes -- 1046;5 Exercises -- CH36;11 Models of power45;law45;type behavior -- 1146;1 Models for heavy45;tailed distribution -- 1146;2 Models for 147; fb processes -- 1146;3 Applications -- 1146;4 Bibliographic notes -- 1146;5 Exerci