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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| Дата: | 2007 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2007
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/4497 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862531685292179456 |
|---|---|
| author | Torbin, G. |
| author_facet | Torbin, G. |
| 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. |
| collection | DSpace DC |
| 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.
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| first_indexed | 2025-11-24T05:32:58Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-4497 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0321-3900 |
| language | English |
| last_indexed | 2025-11-24T05:32:58Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Torbin, G. 2009-11-19T10:27:51Z 2009-11-19T10:27:51Z 2007 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 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. en Інститут математики НАН України Probability distributions with independent Q-symbols and transformations preserving the Hausdorff dimension Article published earlier |
| spellingShingle | Probability distributions with independent Q-symbols and transformations preserving the Hausdorff dimension Torbin, G. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/4497 |
| work_keys_str_mv | AT torbing probabilitydistributionswithindependentqsymbolsandtransformationspreservingthehausdorffdimension |