ENGLISH

Scaling, Fractals and Wavelets

By Patrice Abry , Paolo Goncalves , Jacques Levy Vehel

Book information

Publisher
ISTE Ltd
Year
2009
ISBN
9781848210721
LCC
TK5102.9 .L65 2007
Open Library ID
OL16833415M
Language
english
Format
PDF
Filesize
4 MB (4632681 bytes)
Pages
506\506
Library
Kolxo3
Time added
2010-05-31 15:29:46
Приборостроение;Обработка сигналов;Вейвлет-анализ

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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