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Multifractals and 1/ƒ Noise

Wild Self-Affinity in Physics (1963–1976)

  • Book
  • © 1999

Overview

Authors:
  1. Benoit B. Mandelbrot

    1. Mathematics Department, Yale University, New Haven, USA
      T.J. Watson Research Center, IBM, Yorktown Heights, USA

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-15
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  2. Introductions and Short Pieces

    1. Front Matter

      Pages 17-17
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    2. Panorama of grid-bound self-affine variability

      • Benoit B. Mandelbrot
      Pages 18-61

    3. Sketches of prehistory and history

      • Benoit B. Mandelbrot
      Pages 62-99

    4. Scaling, invariants and fixed points

      • Benoit B. Mandelbrot
      Pages 100-110

    5. Filtering and specification of self-affinity

      • Benoit B. Mandelbrot
      Pages 111-116

    6. Short excerpts (1964–1984)

      • Benoit B. Mandelbrot
      Pages 117-130

  3. Unifractal Errors and Lévy Dusts

    1. Front Matter

      Pages 131-131
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    2. New model for the clustering of errors on telephone circuits (Berger & M 1963)

      • Benoit B. Mandelbrot
      Pages 132-165

    3. Self-similarity and conditional stationarity

      • Benoit B. Mandelbrot
      Pages 166-205

  4. Intermittent 1/ƒ Noises and Conditioned Random Processes

    1. Front Matter

      Pages 207-207
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    2. 1/ƒ noises and the infrared catastrophe

      • Benoit B. Mandelbrot
      Pages 208-214

    3. Co-indicator functions and related 1/ƒ noises

      • Benoit B. Mandelbrot
      Pages 215-246

    4. Sporadic random functions and conditional spectra; self-similar examples and limits

      • Benoit B. Mandelbrot
      Pages 247-283

    5. Random sets of multiplicity for trigonometric series (Kahane & M 1965)

      • Benoit B. Mandelbrot
      Pages 284-288

  5. Turbulence and Multifractals

    1. Front Matter

      Pages 289-289
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    2. Sporadic turbulence

      • Benoit B. Mandelbrot
      Pages 290-291

    3. Intermittent free turbulence

      • Benoit B. Mandelbrot
      Pages 292-293

    4. Lognormal hypothesis and distribution of energy dissipation in intermittent turbulence

      • Benoit B. Mandelbrot
      Pages 294-316

    5. Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier

      • Benoit B. Mandelbrot
      Pages 317-357
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Keywords

About this book

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.

Authors and Affiliations

  • Mathematics Department, Yale University, New Haven, USA

    Benoit B. Mandelbrot

  • T.J. Watson Research Center, IBM, Yorktown Heights, USA

    Benoit B. Mandelbrot

Bibliographic Information

  • Book Title: Multifractals and 1/ƒ Noise

  • Book Subtitle: Wild Self-Affinity in Physics (1963–1976)

  • Authors: Benoit B. Mandelbrot

  • DOI: https://doi.org/10.1007/978-1-4612-2150-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Benoit B. Mandelbrot 1999

  • Softcover ISBN: 978-1-4612-7434-6Published: 03 January 2014

  • eBook ISBN: 978-1-4612-2150-0Published: 20 December 2013

  • Edition Number: 1

  • Number of Pages: VIII, 442

  • Number of Illustrations: 6 b/w illustrations

  • Topics: Topology

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