dorsal/arxiv
View SchemaStochastic models which separate fractal dimension and Hurst effect
| Authors | Tilmann Gneiting, Martin Schlather |
|---|---|
| Categories | |
| ArXiv ID | physics/0109031 |
| URL | https://arxiv.org/abs/physics/0109031 |
| DOI | 10.1137/S0036144501394387 |
| Journal | SIAM Review 46 (2004), 269-282 |
Abstract
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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"abstract": "Fractal behavior and long-range dependence have been observed in an\nastonishing number of physical systems. Either phenomenon has been modeled by\nself-similar random functions, thereby implying a linear relationship between\nfractal dimension, a measure of roughness, and Hurst coefficient, a measure of\nlong-memory dependence. This letter introduces simple stochastic models which\nallow for any combination of fractal dimension and Hurst exponent. We\nsynthesize images from these models, with arbitrary fractal properties and\npower-law correlations, and propose a test for self-similarity.",
"arxiv_id": "physics/0109031",
"authors": [
"Tilmann Gneiting",
"Martin Schlather"
],
"categories": [
"physics.data-an",
"math.PR",
"nlin.CD"
],
"doi": "10.1137/S0036144501394387",
"journal_ref": "SIAM Review 46 (2004), 269-282",
"title": "Stochastic models which separate fractal dimension and Hurst effect",
"url": "https://arxiv.org/abs/physics/0109031"
},
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