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Probability distributions with
independent $Q$-symbols and
transformations preserving the
Hausdorff dimension
Grygoriy Torbin Institut für Angewandte Mathematik, Universität Bonn, Bonn, Germany; National Pedagogical University, Kyiv, Ukraine; Institute
for Mathematics of NASU, Kyiv.
Аннотация:
The paper is devoted to the study of connections between fractal
properties of one-dimensional singularly continuous probability measures and the preservation of the Hausdorff dimension of any subset
of the unit interval under the corresponding distribution function.
Conditions for the distribution function of a random variable with
independent $Q$-digits to be a transformation preserving the Hausdorff dimension (DP-transformation) are studied in details. It is
shown that for a large class of probability measures the distribution function is a DP-transformation if and only if the corresponding
probability measure is of full Hausdorff dimension.
Ключевые слова:
Singularly continuous probability distributions, Hausdorff dimension of probability measures, Hausdorff-Billingsley dimension, fractals, DP-transformations.
Образец цитирования:
Grygoriy Torbin, “Probability distributions with
independent $Q$-symbols and
transformations preserving the
Hausdorff dimension”, Theory Stoch. Process., 13(29):2 (2007), 281–293
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/thsp205 https://www.mathnet.ru/rus/thsp/v13/i2/p281
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Страница аннотации: | 84 | PDF полного текста: | 42 | Список литературы: | 19 |
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