Scaling, Fractals and Wavelets

by Patrice Abry (Editor), Paolo Goncalves (Editor), Jacques Lévy Véhel (Editor)

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 image processing, financial and stock market fluctuations, geophysics, scale relativity, and fractal time-space.

464 pages, Hardcover

First published December 1, 2008