Scaling, Fractals and Wavelets

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.