RELATIONSHIP BETWEEN THE PARAMETERS OF SELF-SIMILARITY, STABILITY AND LONG-RANGE DEPENDENCY OF FRACTAL LEV MOTION
Keywords:fractal Lev motion, self-similarity, long-range dependency, stable distributions, relationship indexes.
AbstractThe problem of searching relationships between the parameters of self-similarity, stability and long-range dependency of fractal Lev motion
is considered. It was proposed to use indexes, constructed by means a model of symmetric mixing of latent factors as a measure of the
relationship between increments of fractal Lev motion process. This approach make it possible to solve the problem of inability to use the
correlation method for estimating such increments caused by the absence of the required distribution moments. Dependence of the relationship index of neighboring increments on the indices of stability and self-similarity is obtained. This dependence has the form of an algebraic equation which has no an explicit solution generally, but can be easily solved numerically. A mathematical model that allows to construct a discrete analogue of the autocorrelation function for the fractal Lev motion is proposed. This model has the form of the system of algebraic equations. It is shown that all of the similar dependencies known for the particular cases of the fractal Lev motion, are special cases of the models obtained in the work. Proposed models allows us to determine any of the three parameters (self-similarity, stability and long-range dependency) on two other that will essentially simplify the modeling and studying stochastic processes having the form of fractal Levý motion.
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