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Multiscale analysis of complex time series [[electronic resource] ] : integration of chaos and random fractal theory, and beyond / / Jianbo Gao ... [et al.]
| Multiscale analysis of complex time series [[electronic resource] ] : integration of chaos and random fractal theory, and beyond / / Jianbo Gao ... [et al.] |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley-Interscience, c2007 |
| Descrizione fisica | 1 online resource (368 p.) |
| Disciplina |
519.5/5
621.3822 |
| Altri autori (Persone) | GaoJianbo <1966-> |
| Soggetto topico |
Time-series analysis
Chaotic behavior in systems Fractals |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-280-97446-X
9786610974467 0-470-19165-1 0-470-19164-3 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910143568303321 |
| Hoboken, N.J., : Wiley-Interscience, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Multiscale analysis of complex time series [[electronic resource] ] : integration of chaos and random fractal theory, and beyond / / Jianbo Gao ... [et al.]
| Multiscale analysis of complex time series [[electronic resource] ] : integration of chaos and random fractal theory, and beyond / / Jianbo Gao ... [et al.] |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley-Interscience, c2007 |
| Descrizione fisica | 1 online resource (368 p.) |
| Disciplina |
519.5/5
621.3822 |
| Altri autori (Persone) | GaoJianbo <1966-> |
| Soggetto topico |
Time-series analysis
Chaotic behavior in systems Fractals |
| ISBN |
1-280-97446-X
9786610974467 0-470-19165-1 0-470-19164-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910830744303321 |
| Hoboken, N.J., : Wiley-Interscience, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Multiscale analysis of complex time series : integration of chaos and random fractal theory, and beyond / / Jianbo Gao ... [et al.]
| Multiscale analysis of complex time series : integration of chaos and random fractal theory, and beyond / / Jianbo Gao ... [et al.] |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley-Interscience, c2007 |
| Descrizione fisica | 1 online resource (368 p.) |
| Disciplina | 519.5/5 |
| Altri autori (Persone) | GaoJianbo <1966-> |
| Soggetto topico |
Time-series analysis
Chaotic behavior in systems Fractals |
| ISBN |
1-280-97446-X
9786610974467 0-470-19165-1 0-470-19164-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910877313403321 |
| Hoboken, N.J., : Wiley-Interscience, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||