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Scaling, Fractals And Wavelets - 9781848210721

Un libro in lingua di Abry Patrice (EDT) Goncalves Paulo (EDT) Vehel Jacques Levy (EDT) edito da John Wiley & Sons Inc, 2008

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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.

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