Office of Academic Resources
Chulalongkorn University
Chulalongkorn University

Home / Help

AuthorMandelbrot, Benoit B. author
TitleMultifractals and 1/ฦ{146} Noise [electronic resource] : Wild Self-Affinity in Physics (1963-1976) / by Benoit B. Mandelbrot
ImprintNew York, NY : Springer New York : Imprint: Springer, 1999
Connect to
Descript VIII, 442 p. online resource


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

Mathematics Topology Mathematics Topology


Office of Academic Resources, Chulalongkorn University, Phayathai Rd. Pathumwan Bangkok 10330 Thailand

Contact Us

Tel. 0-2218-2929,
0-2218-2927 (Library Service)
0-2218-2903 (Administrative Division)
Fax. 0-2215-3617, 0-2218-2907

Social Network


facebook   instragram