Scaling, Fractals and Wavelets

Scaling, Fractals and Wavelets

Editor(s): Patrice Abry, Paulo Gonçalves, Jacques Lévy Véhel

Published Online: 2 FEB 2010

Print ISBN: 9781848210721

Online ISBN: 9780470611562

DOI: 10.1002/9780470611562

About this Book

Scaling is a mathematical transformation that enlarges or diminishes objects. The technique is used in a variety of areas, including finance and image processing. This book is organized around the notions of scaling phenomena and scale invariance. The various stochastic models commonly used to describe scaling ? self-similarity, long-range dependence and multi-fractals ? are introduced. These models are compared and related to one another. Next, fractional integration, a mathematical tool closely related to the notion of scale invariance, is discussed, and stochastic processes with prescribed scaling properties (self-similar processes, locally self-similar processes, fractionally filtered processes, iterated function systems) are defined. A number of applications where the scaling paradigm proved fruitful are detailed: image processing, financial and stock market fluctuations, geophysics, scale relativity, and fractal time-space.

Table of contents

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    2. Chapter 8

      Fractional Synthesis, Fractional Filters (pages 279–299)

      Liliane Bel, Georges Oppenheim, Luc Robbiano and Marie-Claude Viano

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