TY  - JOUR
ID  - epos214
UR  - http://dx.doi.org/10.1137/S0036144501394387
IS  - 2
A1  - Gneiting, Tilmann
A1  - Schlather, Martin
N2  - 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.
VL  - 46
TI  - Stochastic Models That Separate Fractal Dimension and the Hurst Effect
AV  - none
EP  - 282
Y1  - 2004///
PB  - Society for Industrial and Applied Mathematics
JF  - SIAM Review
KW  - Cauchy class
KW  -  fractal dimension
KW  -  fractional Brownian motion
KW  -  Hausdor? dimension
KW  - 
Hurst coe?cient
KW  -  long-range dependence
KW  -  power-law covariance
KW  -  self-similar
KW  -  simulation
SN  - 0036-1445
SP  - 269
ER  -