Multiscale analysis of complex time series [[electronic resource] ] : integration of chaos and random fractal theory, and beyond / / Jianbo Gao ... [et al.]

• Record Nr.: UNINA9910830744303321
• Pubbl/distr/stampa: Hoboken, N.J., : Wiley-Interscience, c2007
• ISBN: 1-280-97446-X; 9786610974467; 0-470-19165-1; 0-470-19164-3
• Descrizione fisica: 1 online resource (368 p.)
• Altri autori (Persone): GaoJianbo <1966->
• Disciplina: 519.5/5; 621.3822
• Soggetti: Time-series analysis; Chaotic behavior in systems; Fractals
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. 319-346) and index.
• Nota di contenuto: Multiscale Analysis of Complex Time Series; CONTENTS; Preface; 1 Introduction; 1.1 Examples of multiscale phenomena; 1.2 Examples of challenging problems to be pursued; 1.3 Outline of the book; 1.4 Bibliographic notes; 2 Overview of fractal and chaos theories; 2.1 Prelude to fractal geometry; 2.2 Prelude to chaos theory; 2.3 Bibliographic notes; 2.4 Warmup exercises; 3 Basics of probability theory and stochastic processes; 3.1 Basic elements of probability theory; 3.1.1 Probability system; 3.1.2 Random variables; 3.1.3 Expectation; 3.1.4 Characteristic function, moment generating function, Laplace transform, and probability generating function3.2 Commonly used distributions; 3.3 Stochastic processes; 3.3.1 Basic definitions; 3.3.2 Markov processes; 3.4 Special topic: How to find relevant information for a new field quickly; 3.5 Bibliographic notes; 3.6 Exercises; 4 Fourier analysis and wavelet multiresolution analysis; 4.1 Fourier analysis; 4.1.1 Continuous-time (CT) signals; 4.1.2 Discrete-time (DT) signals; ; 4.1.3 Sampling theorem; 4.1.4 Discrete Fourier transform; 4.1.5 Fourier analysis of real data; 4.2 Wavelet multiresolution analysis4.3 Bibliographic notes; 4.4 Exercises; 5 Basics of fractal geometry; 5.1 The notion of dimension; 5.2 Geometrical fractals; 5.2.1 Cantor sets; 5.2.2 Von Koch curves; 5.3 Power law and perception of self-similarity; 5.4 Bibliographic notes; 5.5 Exercises; 6 Self-similar stochastic processes; 6.1 General definition; 6.2 Brownian motion (Bm); 6.3 Fractional Brownian motion (fBm); 6.4 Dimensions of Bm and fBm processes; 6.5 Wavelet representation of fBm processes; 6.6 Synthesis of fBm processes; 6.7 Applications; 6.7.1 Network traffic modeling; 6.7.2 Modeling of rough surfaces6.8 Bibliographic notes; 6.9 Exercises; 7 Stable laws and Levy motions; 7.1 Stable distributions; 7.2 Summation of strictly stable random variables; 7.3 Tail probabilities and extreme events; 7.4 Generalized central limit theorem; 7.5 Levy motions; 7.6 Simulation of stable random variables; 7.7 Bibliographic notes; 7.8 Exercises; 8 Long memory processes and structure-function-based multifractal analysis; 8.1 Long memory: basic definitions; 8.2 Estimation of the Hurst parameter; 8.3 Random walk representation and structure-function-based multifractal analysis; 8.3.1 Random walk representation8.3.2 Structure-function-based multifractal analysis; 8.3.3 Understanding the Hurst parameter through multifractal analysis; 8.4 Other random walk-based scaling parameter estimation; 8.5 Other formulations of multifractal analysis; 8.6 The notion of finite scaling and consistency of H estimators; 8.7 Correlation structure of ON/OFF intermittency and Levy motions; 8.7.1 Correlation structure of ON/OFF intermittency; 8.7.2 Correlation structure of Levy motions; 8.8 Dimension reduction of fractal processes using principal component analysis; 8.9 Broad applications; 8.9.1 Detection of low observable targets within sea clutter
• Sommario/riassunto: The only integrative approach to chaos and random fractal theory 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. Adopting a data-driven approach, the book c