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E-raamat: Multifractals and 1/ Noise: Wild Self-Affinity in Physics (1963-1976)

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  • Formaat: PDF+DRM
  • Ilmumisaeg: 20-Dec-2013
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9781461221500
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Multifractals and 1/ Noise: Wild Self-Affinity in Physics (1963-1976)Suurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 20-Dec-2013
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9781461221500
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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.

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Preface.- Panorama of grid-bound self affine variablity.- Sketches of
prehistory and history.- Scaling, invariants and fixed points.- Filtering and
specifications of self-affinity.- Short pieces.- New model for error
clustering on telephone circuits.- Additional tests on clustering.-
Self-similarity and conditional stationarity.- 1/f noises and the infrared
catastrophe.- Co-indicator functions and related 1/f noises.- Sporadic random
functions and conditional spectra: Self-similar examples and limits.- Random
sets of multiplicity for trigonometric series.- Sporadic turbulence.-
Intermittent free turbulence.- Lognormal hypothesis and distribution of
energy dissipation in intermittent turbulence.- Intermittent turbulence in
self-similar cascades: Divergence of high moments and dimension of the
carrier.- Iterated random multiplications and invariance under randomly
weighted averaging.- 'On certain martingales of Benoit Mandelbrot'.-
Intermittent turbulence and fractal dimension: the kurtosis and the spectral
exponent 5 3 + B.- Fractal dimension, dispersion, and singularities of fluid
motion.- Elementary fractals and multifractals.- Bibliography.- Index.
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