Scaling, Fractals and Wavelets
Published on 1. March 2013
464 pages
978-1-118-62290-2 (ISBN)
Description
Scaling is a mathematical transformation that enlarges ordiminishes objects. The technique is used in a variety of areas,including finance and image processing. This book is organizedaround the notions of scaling phenomena and scale invariance. Thevarious stochastic models commonly used to describe scaling ?self-similarity, long-range dependence and multi-fractals ? areintroduced. These models are compared and related to one another.Next, fractional integration, a mathematical tool closely relatedto the notion of scale invariance, is discussed, and stochasticprocesses with prescribed scaling properties (self-similarprocesses, locally self-similar processes, fractionally filteredprocesses, iterated function systems) are defined. A number ofapplications where the scaling paradigm proved fruitful aredetailed: image processing, financial and stock marketfluctuations, geophysics, scale relativity, and fractal time-space.
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Patrice Abry | Paolo Goncalves | Jacques Levy Vehel
Scaling, Fractals and Wavelets
Book
01/2009
1st Edition
Wiley-ISTE
€255.50
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Persons
Patrice Abry is a Professor in the Laboratoire de Physiqueat the Ecole Normale Superieure de Lyon, France. His currentresearch interests include wavelet-based analysis and modelling ofscaling phenomena and related topics, stable processes,multi-fractal, long-range dependence, local regularity ofprocesses, infinitely divisible cascades and departures from exactscale invariance.
Paulo Goncalves graduated from the Signal ProcessingDepartment of ICPI, Lyon, France in 1993. He received the Masters(DEA) and Ph.D. degrees in signal processing from the InstitutNational Polytechnique, Grenoble, France, in 1990 and 1993respectively. While working toward his Ph.D. degree, he was withEcole Normale Superieure, Lyon. In 1994-96, he was a PostdoctoralFellow at Rice University, Houston, TX. Since 1996, he is associateresearcher at INRIA, first with Fractales (1996-99), and then witha research team at INRIA Rhone-Alpes (2000-2003). His researchinterests are in multiscale signal and image analysis, inwavelet-based statistical inference, with application tocardiovascular research and to remote sensing for land coverclassification.
Jacques Levy Vehel graduated from Ecole Polytechnique in1983 and from Ecole Nationale Superieure des Telecommuncations in1985. He holds a Ph.D in Applied Mathematics from Universited'Orsay. He is currently a research director at INRIA,Rocquencourt, where he created the Fractales team, a research groupdevoted to the study of fractal analysis and its applications tosignal/image processing. He also leads a research team at IRCCYN,Nantes, with the same scientific focus. His current researchinterests include (multi)fractal processes, 2-microlocal analysisand wavelets, with application to Internet traffic, imageprocessing and financial data modelling.
