Scaling, Fractals and Wavelets |
|
| Editor:
| Abry, Patrice
Goncalves, Paolo
Vehel, Jacques Levy |
| ISBN: | 978-1-118-62290-2 |
| Publication Date: | Mar 2013 |
| Publisher: | John Wiley & Sons, Incorporated
|
| Imprint: | Wiley-ISTE |
| Book Format: | Digital download |
| List Price: | Contact Supplier contact
Contact Supplier contact
|
Book 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...
More 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.