Central limit theorem for centered frequencies of a countable ergodic markov chain
On the basis of results relating to the behavior of the potential of a countable ergodic Markov chain, for a certain class of functions, the asymptotic normality of a variable $\cfrac{1}{\sqrt{n}}\sum^{n-1}_{k=0}f(X_k)$ for $n \rightarrow \infty$ has been proved. The asymptotic normality of the ce...
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| Date: | 1993 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
1993
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5982 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512205255999488 |
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| author | Moskal'tsova, N. V. Shurenkov, V. M. Москальцова, Н. В. Шуренков, В. М. Москальцова, Н. В. Шуренков, В. М. |
| author_facet | Moskal'tsova, N. V. Shurenkov, V. M. Москальцова, Н. В. Шуренков, В. М. Москальцова, Н. В. Шуренков, В. М. |
| author_sort | Moskal'tsova, N. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:22:20Z |
| description | On the basis of results relating to the behavior of the potential of a countable ergodic Markov chain, for a certain class of functions, the asymptotic normality of a variable
$\cfrac{1}{\sqrt{n}}\sum^{n-1}_{k=0}f(X_k)$ for $n \rightarrow \infty$ has been proved.
The asymptotic normality of the centering frequencies has been obtained without using the finileness conditions for the time $M_0\tau^2$ of the first return into a chain state. |
| first_indexed | 2026-03-24T03:25:05Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5982 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:25:05Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/b7/c0739e15590ba82093c7b3c11f0f51b7.pdf |
| spelling | umjimathkievua-article-59822020-03-19T09:22:20Z Central limit theorem for centered frequencies of a countable ergodic markov chain Центральная предельная теорема для центрированных частот счетной эргодической цепи Маркова Moskal'tsova, N. V. Shurenkov, V. M. Москальцова, Н. В. Шуренков, В. М. Москальцова, Н. В. Шуренков, В. М. On the basis of results relating to the behavior of the potential of a countable ergodic Markov chain, for a certain class of functions, the asymptotic normality of a variable $\cfrac{1}{\sqrt{n}}\sum^{n-1}_{k=0}f(X_k)$ for $n \rightarrow \infty$ has been proved. The asymptotic normality of the centering frequencies has been obtained without using the finileness conditions for the time $M_0\tau^2$ of the first return into a chain state. На підставі результатів, що стосуються поведінки потенціалу зліченного ергодичного ланцюга Маркова для певного класу функцій, доведено асимптотичну нормальність величини $\cfrac{1}{\sqrt{n}}\sum^{n-1}_{k=0}f(X_k)$ при $n \rightarrow \infty$. Асимптотичну нормальність центрованих частот здобуто без застосування умови скінченності моменту $M_0\tau^2$ часу першого повернення до стану ланцюга. Institute of Mathematics, NAS of Ukraine 1993-12-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5982 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 12 (1993); 1713–1715 Український математичний журнал; Том 45 № 12 (1993); 1713–1715 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5982/8647 https://umj.imath.kiev.ua/index.php/umj/article/view/5982/8648 Copyright (c) 1993 Moskal'tsova N. V.; Shurenkov V. M. |
| spellingShingle | Moskal'tsova, N. V. Shurenkov, V. M. Москальцова, Н. В. Шуренков, В. М. Москальцова, Н. В. Шуренков, В. М. Central limit theorem for centered frequencies of a countable ergodic markov chain |
| title | Central limit theorem for centered frequencies of a countable ergodic markov chain |
| title_alt | Центральная предельная теорема для центрированных частот счетной эргодической цепи Маркова |
| title_full | Central limit theorem for centered frequencies of a countable ergodic markov chain |
| title_fullStr | Central limit theorem for centered frequencies of a countable ergodic markov chain |
| title_full_unstemmed | Central limit theorem for centered frequencies of a countable ergodic markov chain |
| title_short | Central limit theorem for centered frequencies of a countable ergodic markov chain |
| title_sort | central limit theorem for centered frequencies of a countable ergodic markov chain |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5982 |
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