Stochastic models that separate fractal dimension and the Hurst effect


Gneiting, Tilmann ; Schlather, Martin



Document Type: Article
Year of publication: 2004
The title of a journal, publication series: SIAM Review
Volume: 46
Issue number: 2
Page range: 269-282
Place of publication: Philadelphia, Pa.
Publishing house: SIAM
ISSN: 0036-1445
Publication language: English
Institution: School of Business Informatics and Mathematics > Mathematische Statistik (Schlather 2012-)
Subject: 310 Statistics
510 Mathematics
Keywords (English): Cauchy class, fractal dimension, fractional Brownian motion, Hausdor_ dimension, Hurst coe_cient, long-range dependence, power-law covariance, self-similar, simulation
Abstract: Fractal behavior and long-range dependence have been observed in an astonishing number of physical, biological, geological, and socio-economic systems. Time series, pro_les, and sur- faces have been characterized by their fractal dimension, a measure of roughness, and by the Hurst coe_cient, a measure of long-memory dependence. Either phenomenon has been modeled and explained by self-a_ne random functions, such as fractional Gaussian noise and fractional Brownian motion. The assumption of statistical self-a_nity implies a linear relationship be- tween fractal dimension and Hurst coe_cient and thereby links the two phenomena. This article introduces stochastic models that allow for any combination of fractal dimension and Hurst coe_cient. Associated software for the synthesis of images with arbitrary, pre-speci_ed fractal properties and power-law correlations is available. The new models suggest a test for self-a_nity that assesses coupling and decoupling of local and global behavior.

Dieser Datensatz wurde nicht während einer Tätigkeit an der Universität Mannheim veröffentlicht, dies ist eine Externe Publikation.




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