Geodesic
Topological, metric and fractal
Teoriâ slučajnyh processov, Tome 13 (2007) no. 2, pp. 205-224

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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-Billingsley dimension, fractals, characteristic function of random variable, transformations preserving fractal dimensions.
Mots-clés : Hausdorff-Besicovitch dimension 
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     author = {M. Pratsiovytyi and O. Yu. Feshchenko},
     title = {Topological, metric and fractal},
     journal = {Teori\^a slu\v{c}ajnyh processov},
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     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2007_13_2_a4/}
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M. Pratsiovytyi; O. Yu. Feshchenko. Topological, metric and fractal. Teoriâ slučajnyh processov, Tome 13 (2007) no. 2, pp. 205-224. http://geodesic.mathdoc.fr/item/THSP_2007_13_2_a4/