On asymptotics of the potential of a countable ergodic Markov chain
For a class of functions $f$, the convergence in Abel's sense is proved for the potential $\sum_{n⩾o}P^nf(i) of a uniform ergodic Markov chain in a countable phase space. Several corollaries are obtained which are useful from the point of view of the possible application to CLT (the central...
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| Datum: | 1993 |
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| Hauptverfasser: | , , , |
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| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1993
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5808 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512030415388672 |
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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 | 2020-03-19T09:18:17Z |
| description | For a class of functions $f$, the convergence in Abel's sense is proved for the potential $\sum_{n⩾o}P^nf(i) of a uniform ergodic Markov chain in a countable phase space. Several corollaries are obtained which are useful from the point of view of the possible application to CLT (the central limit theorem) for Markov chains. In particular, we establish the condition equivalent to the boundedness of the second moment for the time of the first return into the state. |
| first_indexed | 2026-03-24T03:22:18Z |
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| id | umjimathkievua-article-5808 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:22:18Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/c2/ac327f9490698295732329e4eec35bc2.pdf |
| spelling | umjimathkievua-article-58082020-03-19T09:18:17Z On asymptotics of the potential of a countable ergodic Markov chain Об асимптотике потенциала счет ной эргодической цепи Маркова Moskal'tsova, N. V. Shurenkov, V. M. Москальцова, Н. В. Шуренков, В. М. Москальцова, Н. В. Шуренков, В. М. For a class of functions $f$, the convergence in Abel's sense is proved for the potential $\sum_{n⩾o}P^nf(i) of a uniform ergodic Markov chain in a countable phase space. Several corollaries are obtained which are useful from the point of view of the possible application to CLT (the central limit theorem) for Markov chains. In particular, we establish the condition equivalent to the boundedness of the second moment for the time of the first return into the state. Для певного класу функцій $f$ доведено збіжність за Абелем потенціалу $\sum_{n⩾o}P^nf(i)$ однорідного ергодичного ланцюга Маркова в зліченному фазовому просторі. Зроблено ряд висновків, корисних для погреб ЦГТ для ланцюгів Маркова, зокрема, умова, еквівалентна скінченносіі другого моменту для часу першого повернення до стану. Institute of Mathematics, NAS of Ukraine 1993-02-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5808 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 2 (1993); 265–269 Український математичний журнал; Том 45 № 2 (1993); 265–269 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5808/8299 https://umj.imath.kiev.ua/index.php/umj/article/view/5808/8300 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. On asymptotics of the potential of a countable ergodic Markov chain |
| title | On asymptotics of the potential of a countable ergodic Markov chain |
| title_alt | Об асимптотике потенциала счет ной эргодической цепи Маркова |
| title_full | On asymptotics of the potential of a countable ergodic Markov chain |
| title_fullStr | On asymptotics of the potential of a countable ergodic Markov chain |
| title_full_unstemmed | On asymptotics of the potential of a countable ergodic Markov chain |
| title_short | On asymptotics of the potential of a countable ergodic Markov chain |
| title_sort | on asymptotics of the potential of a countable ergodic markov chain |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5808 |
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