Stochastic models which separate fractal dimension and Hurst effect

Details Stochastic models which separate fractal dimension and Hurst effect Stochastic models which separate fractal dimension and Hurst effect

2001-09-13

arxiv.org/abs/physics/0109031v1

SIAM Review 46 (2004), 269-282

Physics

Data Analysis, Statistics and Probability

8 pages, 2 figures

Scientific paper

Fractal behavior and long-range dependence have been observed in an astonishing number of physical systems. Either phenomenon has been modeled by self-similar random functions, thereby implying a linear relationship between fractal dimension, a measure of roughness, and Hurst coefficient, a measure of long-memory dependence. This letter introduces simple stochastic models which allow for any combination of fractal dimension and Hurst exponent. We synthesize images from these models, with arbitrary fractal properties and power-law correlations, and propose a test for self-similarity.

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