Multiscale analysis of complex time series : integration of chaos and random fractal theory, and beyond - Gao, Jianbo, 1966- (Hoboken, N.J. : Wiley-Interscience, 2007)
Overview of fractal and chaos theories -- Basics of probability theory and stochastic processes -- Fourier analysis and wavelet multiresolution analysis -- Basics of fractal geometry -- Self-similar stochastic processes -- Stable laws and levy motions -- Long memory processes and structure-function-based multifractal analysis -- Multiplicative multifractals -- Stage-dependent multiplicative processes -- Models of power-law-type behavior -- Bifurcation theory -- Chaotic time series analysis -- Power-law sensitivity to initial conditions (PSIC) -- Multiscale analysis by the scale-dependent lyapunov exponent (SDLE) -- Appendix A. Description of data -- Appendix B. Principal component analysis (PCA), singular value decomposition (SVD), and Karhunen-loeve (KL) expansion -- Appendix C. Complexity measures
Includes bibliographical references (p. 319-346) and index
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Keywords: Chaos; Chaotic behavior in systems; Fractales; Fractals; Serie chronologique; Time-series analysis