Scaling, Fractals and Wavelets
- ISBN-10
- 1118622901
- ISBN-13
- 9781118622902
- Category
- Mathematics
- Pages
- 464
- Language
- English
- Published
- 2013-03-01
- Publisher
- John Wiley & Sons
- Authors
- Jacques Levy Vehel, Patrice Abry, Paolo Goncalves
Description
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.
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