Remarks on summability of series formed of deviation probabilities of sums of independent identically distributed random variables
We make some remarks leading to a refinement of the recent work of Klesov (1993) on the connection between the convergence of the series \(\Sigma _{n = 1}^\infty \tau _n P(|S_n | \ge \varepsilon n^\alpha )\) for every ε > 0 and the convergence of \(\Sigma _{n = 1}^\infty n\tau _n P(|X_1...
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| Дата: | 1996 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1996
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/5323 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511542441672704 |
|---|---|
| author | Pruss, A. R. Прус, А. Р. |
| author_facet | Pruss, A. R. Прус, А. Р. |
| author_sort | Pruss, A. R. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T15:28:54Z |
| description | We make some remarks leading to a refinement of the recent work of Klesov (1993) on the connection between the convergence of the series \(\Sigma _{n = 1}^\infty \tau _n P(|S_n | \ge \varepsilon n^\alpha )\) for every ε > 0 and the convergence of \(\Sigma _{n = 1}^\infty n\tau _n P(|X_1 | \ge \varepsilon n^\alpha )\) again for every ε > 0. |
| first_indexed | 2026-03-24T03:14:33Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5323 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:14:33Z |
| publishDate | 1996 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/f0/9a790597ab153410ad0ca2de6da4b1f0.pdf |
| spelling | umjimathkievua-article-53232020-03-19T15:28:54Z Remarks on summability of series formed of deviation probabilities of sums of independent identically distributed random variables Remarks on summability of series formed of deviation probabilities of sums of independent identically distributed random variables Pruss, A. R. Прус, А. Р. We make some remarks leading to a refinement of the recent work of Klesov (1993) on the connection between the convergence of the series \(\Sigma _{n = 1}^\infty \tau _n P(|S_n | \ge \varepsilon n^\alpha )\) for every ε > 0 and the convergence of \(\Sigma _{n = 1}^\infty n\tau _n P(|X_1 | \ge \varepsilon n^\alpha )\) again for every ε > 0. Одержано результати, що уточнюють недавню роботу О.І. Кльосова (1993) про зв'язок між збіжністю \(\Sigma _{n = 1}^\infty \tau _n P(|S_n | \ge \varepsilon n^\alpha )\) для всіх ε > 0 і збіжністю \(\Sigma _{n = 1}^\infty n\tau _n P(|X_1 | \ge \varepsilon n^\alpha )\) також для всіх ε > 0 . Institute of Mathematics, NAS of Ukraine 1996-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5323 Ukrains’kyi Matematychnyi Zhurnal; Vol. 48 No. 4 (1996); 569-572 Український математичний журнал; Том 48 № 4 (1996); 569-572 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/5323/7337 https://umj.imath.kiev.ua/index.php/umj/article/view/5323/7338 Copyright (c) 1996 Pruss A. R. |
| spellingShingle | Pruss, A. R. Прус, А. Р. Remarks on summability of series formed of deviation probabilities of sums of independent identically distributed random variables |
| title | Remarks on summability of series formed of deviation probabilities of sums of independent identically distributed random variables |
| title_alt | Remarks on summability of series formed of deviation probabilities of sums of independent identically distributed random variables |
| title_full | Remarks on summability of series formed of deviation probabilities of sums of independent identically distributed random variables |
| title_fullStr | Remarks on summability of series formed of deviation probabilities of sums of independent identically distributed random variables |
| title_full_unstemmed | Remarks on summability of series formed of deviation probabilities of sums of independent identically distributed random variables |
| title_short | Remarks on summability of series formed of deviation probabilities of sums of independent identically distributed random variables |
| title_sort | remarks on summability of series formed of deviation probabilities of sums of independent identically distributed random variables |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5323 |
| work_keys_str_mv | AT prussar remarksonsummabilityofseriesformedofdeviationprobabilitiesofsumsofindependentidenticallydistributedrandomvariables AT prusar remarksonsummabilityofseriesformedofdeviationprobabilitiesofsumsofindependentidenticallydistributedrandomvariables |