Scaling, Fractals and WaveletsISBN: 978-1-84821-072-1
Hardcover
464 pages
March 2009, Wiley-ISTE
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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.