  We propose a simple model based on the Gnedenko limit theorem for simulation
and studies of the ordinary Levy motion, that is, a random process, whose
increments are independent and distributed with a stable probability law. We
use the generalized structure function for characterizing anomalous diffusion
rate and propose to explore the modified Hurst method for empirical rescaled
range analysis. We also find that the structure function being estimated from
the ordinary Levy motion sample paths as well as the (ordinary) Hurst method
lead to spurious ''pseudo-Gaussian'' relations.
