Stochastic Models That Separate Fractal Dimension and the Hurst Effect

  title={Stochastic Models That Separate Fractal Dimension and the Hurst Effect},
  author={Tilmann Gneiting and Martin Schlather},
  journal={SIAM Rev.},
Fractal behavior and long-range dependence have been observed in an astonishing number of physical, biological, geological, and socioeconomic systems. Time series, profiles, and surfaces have been characterized by their fractal dimension, a measure of roughness, and by the Hurst coefficient, a measure of long-memory dependence. Both phenomena have been modeled and explained by self-affine random functions, such as fractional Gaussian noise and fractional Brownian motion. The assumption of… 

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