PECULARITIES OF HIRST EXPONENT ESTIMATION FOR NATURAL PHYSICAL PROCESSES
Abstract
In bounds of the non-linear and system paradigms, been formulated by L. F. Chernogor in the last 1980th, all processes in open, non-linear, dynamical systems are very complex, non-linear, ultra-wideband or fractal ones.
According to the fractal paradigm put forward in the early 2000s by V. V. Yanovsky, fractality is one of the fundamental properties of the surrounding world. Therefore, the study of fractal characteristics, in particular, of natural physical processes is actual, interesting and useful.
The fractal dimension based on the Hurst exponent is one of the oldest and most famous ones. Based on the study of model fractal signals, it is demonstrated that the dependence between the estimate of the Hurst fractal dimension, obtained by the normalized range method, and its true value is significantly non-linear. To decrease of influence of the errors arising as a result of this, it is proposed to use the method of the corrective function.
The practical effectiveness of the proposed method is demonstrated on the example of the analysis of experimental results obtained in the middle 1960s by H. E. Hurst, which discovered the presence of a somewhat strange grouping of the values of the Hurst fractal dimension around the value of 1.27 for various natural physical processes. A hypothesis about the possibility of explaining this fact precisely by the nonlinearity of the mentioned dependence for R/S-method was proposed.
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