ANALYSIS OF THE PROPERTIES OF ORDINARY LEVY MOTION BASED ON THE ESTIMATION OF STABILITY INDEX

The work proposes a method for estimating the stability index of alpha-stable distributions by using moments of fractional order. Provided numerical modeling has fully justified all of the results. Comparative analysis of the efficiency among the proposed method of estimating the stability index and widely used methods was performed. Proposal method is much simpler, far faster and substantially less memory required. Estimation of generalized Hurst exponent from time series of the ordinary Levy process was performed. Multifractal fluctuation analysis method and evaluation based on stability index estimation were compared. The results of numerical modeling showed that proposed method for estimating the fractal properties of the ordinary Levy process, based on stability index estimation via fractional order moments is a much more accurate.  , offset, scale and symmetry measures. Estimation of these parameters is a difficult task. This is partly caused by those facts that with few exceptions pdf's and cdf's of stable distributions are not expressed in terms of elementary functions.