Abstract:
We study the structure, topological, metric and fractal properties of
the distribution of random incomplete sum of the convergent positive
series with independent terms under certain conditions on the rate
of convergence of series and on the distributions of its terms. We
also study the behaviour of the absolute value of the characteristic
function of this random variable at infinity and the fractal dimension
preservation by its distribution function.
Keywords:Set of incomplete sums of series, singularly continuous probability distributions, absolutely continuous probability distributions, Hausdorff-Besicovitch dimension, Hausdorff-Billingsley dimension, fractals, characteristic function
of random variable, transformations preserving fractal dimensions.
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