(Ebook) Scaling, Fractals and Wavelets by Patrice Abry, Paulo Gonçalves, Jacques Lévy Véhel ISBN 9781848210721, 1848210728

(Ebook) Scaling, Fractals and Wavelets by Patrice Abry, Paulo Gonçalves, Jacques Lévy Véhel ISBN 9781848210721, 1848210728

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.