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Stochastic models that separate fractal dimension and the Hurst effect
Gneiting, Tilmann
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Schlather, Martin
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Document Type:
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Article
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Year of publication:
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2004
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The title of a journal, publication series:
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SIAM Review
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Volume:
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46
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Issue number:
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2
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Page range:
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269-282
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Place of publication:
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Philadelphia, Pa.
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Publishing house:
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SIAM
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ISSN:
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0036-1445
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Publication language:
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English
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Institution:
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School of Business Informatics and Mathematics > Applied Stochastics (Schlather 2012-)
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Subject:
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310 Statistics
510 Mathematics
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Keywords (English):
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Cauchy class, fractal dimension, fractional Brownian motion, Hausdor_ dimension, Hurst coe_cient, long-range dependence, power-law covariance, self-similar, simulation
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Abstract:
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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.
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 | Dieser Datensatz wurde nicht während einer Tätigkeit an der Universität Mannheim veröffentlicht, dies ist eine Externe Publikation. |
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