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Biomathematics --- Mathematics in nature --- Ecology --- Aquatic sciences --- Fractals --- Multifractals
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Fractals. --- Multifractals. --- Electronic noise. --- Fractales --- Multifractales --- Bruit électronique
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The dynamics of complex systems can clarify the creation of structures in Nature. This creation is driven by the collective interaction of constitutive elements of the system. Such interactions are frequently nonlinear and are directly responsible for the lack of prediction in the evolution process. The self-organization accompanying these processes occurs all around us and is constantly being rediscovered, under the guise of a new jargon, in apparently unrelated disciplines. This volume offers unique perspectives on aspects of fractals and complexity and, through the examination of compleme
Fractals. --- Multifractals. --- Fractals --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Multifractals --- lemac
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Calvet and Fisher present a powerful, new technique for volatility forecasting that draws on insights from the use of multifractals in the natural sciences and mathematics and provides a unified treatment of the use of multifractal techniques in finance. A large existing literature (e.g., Engle, 1982; Rossi, 1995) models volatility as an average of past shocks, possibly with a noise component. This approach often has difficulty capturing sharp discontinuities and large changes in financial volatility. Their research has shown the advantages of modelling volatility as subject to abrupt regime c
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Certain noises, many aspects of turbulence, and almost all aspects of finance exhibit a level of temporal and spatial variability whose "wildness" impressed itself vividly upon the author, Benoit Mandelbrot, in the early 1960's. He soon realized that those phenomena cannot be described by simply adapting the statistical techniques of earlier physics, or even extending those techniques slightly. It appeared that the study of finance and turbulence could not move forward without the recognition that those phenomena represented a new second stage of indeterminism. Altogether new mathematical tools were needed. The papers in this Selecta volume reflect that realization and the work that Dr. Mandelbrot did toward the development of those new tools.
Multifractals --- Electronic noise. --- Multifractales --- Bruit électronique --- Electronic noise --- Bruit électronique --- Topology. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Multifractals. --- Noise, Electronic --- Signal theory (Telecommunication) --- Electric noise --- Fractals
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Geophysics --- Nonlinear theories --- Géophysique --- Théories non linéaires --- Periodicals --- Périodiques --- Earth Sciences --- Engineering --- Mathematical Sciences --- Physics --- General and Others --- Satellites, Space Probes & Technology --- Calculus --- scaling and multifractals --- predictability --- nonlinear waves --- turbulence and diffusion --- chaos and nonlinear time series analysis --- nonlinear systems and dynamics --- Nonlinear theories. --- Geofysica. --- Nonlinear problems --- Nonlinearity (Mathematics) --- Mathematical analysis --- Mathematical physics --- Geological physics --- Terrestrial physics --- Earth sciences
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