Multifractals and 1/f Noise

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 tool

Table des matières
Preface (1998)
I Introductions and Short Pieces
Panorama of grid-bound self-affine variability (1998)
Sketches of prehistory and history (1998)
Scaling, invariants and fixed points (1998)
Filtering and specifications of self-affinity (1998)
Short pieces (1964-1986)
II Unifractal Errors and Levy Dusts
New model for error clustering on telephone circuits (Berger & M 1963). Additional tests on clustering (1998)
Self-similarity and conditional stationarity (M 1965c)
III Intermittent 1/f Noises and Conditioned Random Processes
1 f noises and the infrared catastrophe (M 1965b)
Co-indicator functions and related 1 f noises (M 1967i)
Sporadic random functions and conditional spectra self-similar examples and limits (M 1967b)
Random sets of multiplicity for trigonometric series (Kahane & M 1965)
IV Turbulence and Multifractal Measures
Sporadic turbulence (M 1967k)
Intermittent free turbulence (M 1969b)
Lognormal hypothesis and distribution of energy dissipation in intermittent turbulence (M 1972j)
Intermittent turbulence in self similar cascades divergence of high moments and dimension of the carrier (M 1974f)
Iterated random multiplications and invariance under randomly weighted averaging (M 1974c)
"On certain martingales of Benoit Mandelbrot" Guest contribution (Kahane & Peyriere 1976)
Intermittent turbulence and fractal dimension: the kurtosis and the spectral exponent 5 3 + B (M 1976o)
Fractal dimension, dispersion, and singularities of fluid motion (M 1976c)
V Background
Elementary fractals and multifractals
Bibliography
Index