@article{epos214,
          volume = {46},
          number = {2},
          author = {Tilmann Gneiting and Martin Schlather},
           title = {Stochastic Models That Separate Fractal Dimension and the Hurst Effect},
       publisher = {Society for Industrial and Applied Mathematics},
         journal = {SIAM Review},
           pages = {269--282},
            year = {2004},
        keywords = {Cauchy class, fractal dimension, fractional Brownian motion, Hausdor? dimension,
Hurst coe?cient, long-range dependence, power-law covariance, self-similar, simulation},
             url = {https://episodesplatform.eu/eprints/214/},
        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 surfaces have been characterized by their fractal dimension, a measure of roughness, and by the Hurst coefficient, a measure of long-memory dependence. Either phenomenon has been modeled and explained by self-affine random functions, such as fractional Gaussian noise and fractional Brownian motion. The assumption of statistical self a?nity implies a linear relationship between fractal dimension and Hurst coefficient and thereby links the two phenomena. This article introduces stochastic models that allow for any combination of fractal dimension and Hurst coefficient. 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-affinity that assesses coupling and decoupling of local and global behavior.}
}