Stabilogram diffusion analysis algorithm to estimate the Hurst exponent of high-dimensional fractals
Анотація
We suggest an algorithm for the estimation of the Hurst exponent that is based on the results of the well-known stabilogram diffusion analysis method of Hurst exponent estimation for one-dimensional fractals. Our algorithm can be applied to Hurst exponent estimation for fractals with two or more dimensions. To assess the efficiency of this algorithm, we compare its calculation results to those of the well-known Hurst exponent estimation detrending moving average analysis algorithm. In this paper, the computation of the Hurst exponent has been performed for two-dimensional domains of various sizes, which were generated by the Cholesky–Levinson factorization algorithm. The surrogate surfaces have Hurst exponents of H = 0.1, 0.5, and 0.9. It has been established that the detrending moving average analysis algorithm is more sensitive to high-frequency components, while the stabilogram diffusion analysis tends to be sensitive to low-frequency components.
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