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: | English |
| Опубліковано: |
Інститут математики НАН України
2007
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| Онлайн доступ: | http://dspace.nbuv.gov.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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-4497 |
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irk-123456789-44972009-11-20T12:00:40Z 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 http://dspace.nbuv.gov.ua/handle/123456789/4497 en 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 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/4497 |
| 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. |
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