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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| Datum: | 2007 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2007
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| Zitieren: | 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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oai:nasplib.isofts.kiev.ua:123456789-44972025-02-23T17:40:53Z Probability distributions with independent Q-symbols and transformations preserving the Hausdorff dimension Torbin, G. 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. 2007 Article 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. 0321-3900 https://nasplib.isofts.kiev.ua/handle/123456789/4497 en application/pdf Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Torbin, G. |
| spellingShingle |
Torbin, G. Probability distributions with independent Q-symbols and transformations preserving the Hausdorff dimension |
| author_facet |
Torbin, G. |
| author_sort |
Torbin, G. |
| title |
Probability distributions with independent Q-symbols and transformations preserving the Hausdorff dimension |
| title_short |
Probability distributions with independent Q-symbols and transformations preserving the Hausdorff dimension |
| title_full |
Probability distributions with independent Q-symbols and transformations preserving the Hausdorff dimension |
| title_fullStr |
Probability distributions with independent Q-symbols and transformations preserving the Hausdorff dimension |
| title_full_unstemmed |
Probability distributions with independent Q-symbols and transformations preserving the Hausdorff dimension |
| title_sort |
probability distributions with independent q-symbols and transformations preserving the hausdorff dimension |
| publisher |
Інститут математики НАН України |
| publishDate |
2007 |
| citation_txt |
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. |
| work_keys_str_mv |
AT torbing probabilitydistributionswithindependentqsymbolsandtransformationspreservingthehausdorffdimension |
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2025-07-22T04:26:02Z |
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2025-07-22T04:26:02Z |
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