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Multifractals and 1/ƒ Noise

Wild Self-Affinity in Physics (1963–1976)

  • Benoit B. Mandelbrot

Table of contents

  1. Front Matter
    Pages i-15
  2. Introductions and Short Pieces

    1. Front Matter
      Pages 17-17
    2. Benoit B. Mandelbrot
      Pages 18-61
    3. Benoit B. Mandelbrot
      Pages 62-99
    4. Benoit B. Mandelbrot
      Pages 100-110
    5. Benoit B. Mandelbrot
      Pages 111-116
    6. Benoit B. Mandelbrot
      Pages 117-130
  3. Unifractal Errors and Lévy Dusts

    1. Front Matter
      Pages 131-131
    2. Benoit B. Mandelbrot
      Pages 166-205
  4. Intermittent 1/ƒ Noises and Conditioned Random Processes

    1. Front Matter
      Pages 207-207
    2. Benoit B. Mandelbrot
      Pages 208-214
    3. Benoit B. Mandelbrot
      Pages 215-246
  5. Turbulence and Multifractals

  6. Back Matter
    Pages 419-442

About this book

Introduction

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.

Keywords

DEX Etch Impress Invariant Martingale Self-similarity Variance Volume distribution fractal model sets similarity techniques tool

Authors and affiliations

  • Benoit B. Mandelbrot
    • 1
    • 2
  1. 1.Mathematics DepartmentYale UniversityNew HavenUSA
  2. 2.T.J. Watson Research CenterIBMYorktown HeightsUSA

Bibliographic information