Multifractals and 1/F Noise: Wild Self-Affinity in Physics (1963-1976) : Selecta Volume N

by Mandelbrot, Benoit B.

• ISBN13: 9780387985398
• ISBN10: 0387985395
• Edition: 1st
• Format: Hardcover
• Copyright: 1999-01-01
• Publisher: Springer Verlag

Summary

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.

Table of Contents

NP Preface (1998)	1	(16)
I INTRODUCTIONS AND SHORT PIECES	17	(114)
N1 Panorama of grid-bound self-affine variability (1998)	18	(44)
N2 Sketches of prehistory and history (1998)	62	(38)
N3 Scaling, invariants and fixed points (1998)	100	(11)
N4 Filtering and specifications of self-affinity (1998)	111	(6)
N5 Short excerpts (1964-1986)	117	(14)
II UNIFRACTAL ERRORS AND LEVY DUSTS	131	(76)
N6 New model for error clustering on telephone circuits (Berger & M 1963). Additional tests on clustering (1998)	132	(34)
N7 Self-similarity and conditional stationarity (M 1965c)	166	(41)
III INTERMITTENT 1/f NOISES AND CONDITIONED RANDOM PROCESSES	207	(82)
N8 1/f noises and the infrared catastrophe (M 1965b)	208	(7)
N9 Co-indicator functions and related 1/f noises (M 1967i)	215	(32)
N10 Sporadic random functions and conditional spectra self-similar examples and limits (M 1967b)	247	(37)
N11 Random sets of multiplicity for trigonometric series (Kahane & M 1965)	284	(5)
IV TURBULENCE AND MULTIFRACTAL MEASURES	289	(130)
N12 Sporadic turbulence (M 1967k)	290	(2)
N13 Intermittent free turbulence (M 1969b)	292	(2)
N14 Lognormal hypothesis and distribution of energy dissipation in intermittent turbulence (M 1972j)	294	(23)
N15 Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier (M 1974f)	317	(41)
N16 Iterated random multiplications and invariance under randomly weighted averaging (M 1974c)	358	(14)
N17 "On certain martingales of Benoit Mandelbrot" Guest contribution (Kahane & Peyriere 1976)	372	(17)
N18 Intermittent turbulence and fractal dimension: the kurtosis and the spectral exponent 5/3 + B (M 1976o)	389	(27)
N19 Fractal dimension, dispersion, and singularities of fluid motion (M 1976c)	416	(3)
Cumulative Bibliography	419	(13)
Index	432