Organized around the notions of scaling phenomena and scale invariance, this book introduces the various stochastic models commonly used to describe scaling: self-similarity, long-range dependence, and multi-fractals. In subsequent chapters, these models are compared and related to each other and the tool of fractional integration is introduced. Closing sections detail applications of the scaling paradigm, including image processing, stock market fluctuations, geophysics, scale relativity, and fractal time-space.
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About the Author
Patrice Abry is a professor in the Laboratoire de Physique at the Ecole Normale Supérieure in Lyon, France. Paulo Gonçalvès is an associate researcher at INRIA, both with Fractales and with a research team at INRIA Rhone-Alpes. Jacques Lévy Vehel is currently a research director at INRIA, Rocquencourt, where he created the Fractales team, a research group devoted to the study of fractal analysis and its applications to signal/image processing.
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