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Gaussian distributions complex variables

There is an infinite number of attractors, comprising the set of all the stable distributions. Attractors classify the functional space of probability density functions into regions with different complexity. The complexity of stochastic processes is different for the Gaussian attractor and the stable non-Gaussian attractors. In the Gaussian basin of attraction, finite variance random variables are present. But in the basins of attraction of stable non-Gaussian distributions, random variables with infinite variance can be found. Therefore, distributions with power-law tails are present in the stable non-Gaussian basins of attraction (compare reference 22, chapter 5.4). [Pg.16]


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