Probability distributions with independent Q-symbols and transformations preserving the Hausdorff dimension
The paper is devoted to the study of connections between fractal properties of one-dimensional singularly continuous probability measures and the preservation of the Hausdorf dimension of any subset of the unit interval under the corresponding distribution function. Conditions for the distribution f...
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| Date: | 2007 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2007
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Probability distributions with independent Q-symbols and transformations preserving the Hausdorff dimension/ G. Torbin // Theory of Stochastic Processes. — 2007. — Т. 13 (29), № 1-2. — С. 281-293. — Бібліогр.: 12 назв.— англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | The paper is devoted to the study of connections between fractal properties of one-dimensional singularly continuous probability measures and the preservation of the Hausdorf 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 Hausdorf 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 Hausdorf dimension. |
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