Abry, Patrice
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.
Keywords: jacques; signal; multifractal; levy; processing; methods; holder; exponents; measure; theorems; exponent; function; analysis; stock; price; example; market; purpose; ingredient; measures; regularity; local; first, Imaging Systems & Technology, Business & Finance, Imaging Systems & Technology, Business & Finance
- Editor
- Abry, Patrice
- Goncalves, Paolo
- Vehel, Jacques Levy
- Publisher
- John Wiley and Sons, Inc.
- Publication year
- 2008
- Language
- en
- Edition
- 1
- Series
- ISTE
- Page amount
- 464 pages
- Category
- Natural Sciences
- Format
- Ebook
- eISBN (ePUB)
- 9781118622902
- Printed ISBN
- 9781848210721