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About Scaling, Fractals and Wavelets
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.
Detailed Information
| Author: | Patrice Abry, Paolo Goncalves, Jacques Levy Vehel |
|---|---|
| Publication Year: | 2009 |
| ISBN: | 9781848210721 |
| Pages: | 506 |
| Language: | English |
| File Size: | 4.418 |
| Format: | |
| Price: | FREE |
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