$Multifractals and 1/ƒ Noise - Benoit B. Mandelbrot$

Multifractals and 1/ƒ Noise

Wild Self-Affinity in Physics (1963–1976)

Benoit B. Mandelbrot (Autor)

Buch | Softcover

442 Seiten

2014 | Softcover reprint of the original 1st ed. 1999
Springer-Verlag New York Inc.
978-1-4612-7434-6 (ISBN)

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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.

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.

Co-Autor	J.M. Berger, J.-P. Kahane, J. Peyriere
Zusatzinfo	6 Illustrations, black and white; VIII, 442 p. 6 illus.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-4612-7434-6 / 1461274346
ISBN-13	978-1-4612-7434-6 / 9781461274346
Zustand	Neuware