ENGLISH

Scaling, Fractals and Wavelets

By Patrice Abry , Jacques Levy Vehel , Paulo Gonçalves

Book information

Year
2009
ISBN
1848210728, 9781848210721
LCC
TK5102.9 .L65 2007
Open Library ID
OL16833415M
Language
english
Format
PDF
Filesize
5 MB (5033563 bytes)
Edition
1
Pages
464\506
Scanned
yes
Time added
2011-06-04 13:46:07

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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