Convergence of the series of large-deviation probabilities for sums of independent equally distributed random variables
The series $\sum\nolimits_{n \geqslant 1} {\tau _n P(|S_n | \geqslant \varepsilon n^a )}$ is studied, where $S_n$ are the sums of independent equally distributed random variables, $τ_n$ is a sequence of nonnegative numbers, $α > 0$, and $ɛ > 0$ is an arbitrary positive number. For...
Збережено в:
| Дата: | 1993 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1993
|
| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/5866 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512087944462336 |
|---|---|
| author | Klesov, O. I. Клесов, О. И. Клесов, О. И. |
| author_facet | Klesov, O. I. Клесов, О. И. Клесов, О. И. |
| author_sort | Klesov, O. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:19:41Z |
| description | The series $\sum\nolimits_{n \geqslant 1} {\tau _n P(|S_n | \geqslant \varepsilon n^a )}$ is studied, where $S_n$ are the sums of independent equally distributed random variables, $τ_n$ is a sequence of nonnegative numbers, $α > 0$, and $ɛ > 0$ is an arbitrary positive number. For a broad class of sequences $τ_n$, the necessary and sufficient conditions are established for the convergence of this series for any $ɛ > 0$. |
| first_indexed | 2026-03-24T03:23:13Z |
| format | Article |
| fulltext |
0040
0041
0042
0043
0044
0045
0046
0047
0048
0049
0050
0051
0052
0053
0054
|
| id | umjimathkievua-article-5866 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:23:13Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/c6/7e089ce342d9f5ae93427952543012c6.pdf |
| spelling | umjimathkievua-article-58662020-03-19T09:19:41Z Convergence of the series of large-deviation probabilities for sums of independent equally distributed random variables Сходимость рядов из вероятностей больших уклонений сумм независимых одинаково распределенных случайных величин Klesov, O. I. Клесов, О. И. Клесов, О. И. The series $\sum\nolimits_{n \geqslant 1} {\tau _n P(|S_n | \geqslant \varepsilon n^a )}$ is studied, where $S_n$ are the sums of independent equally distributed random variables, $τ_n$ is a sequence of nonnegative numbers, $α > 0$, and $ɛ > 0$ is an arbitrary positive number. For a broad class of sequences $τ_n$, the necessary and sufficient conditions are established for the convergence of this series for any $ɛ > 0$. Вивчаються ряди $\sum\nolimits_{n \geqslant 1} {\tau _n P(|S_n | \geqslant \varepsilon n^a )}$, де $S_n$ - це суми незалежних однаково розподілених випадкових величин, $τ_n$ - довільна послідовність додатних чисел, $ α> 0, ɛ > 0$ - довільне додатне число. Для широкого класу послідовностей $τ_n$ знайдені необхідні та достатні умови збіжності для будь-якого $ɛ > 0$. цього ряду. Institute of Mathematics, NAS of Ukraine 1993-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5866 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 6 (1993); 770–784 Український математичний журнал; Том 45 № 6 (1993); 770–784 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5866/8415 https://umj.imath.kiev.ua/index.php/umj/article/view/5866/8416 Copyright (c) 1993 Klesov O. I. |
| spellingShingle | Klesov, O. I. Клесов, О. И. Клесов, О. И. Convergence of the series of large-deviation probabilities for sums of independent equally distributed random variables |
| title | Convergence of the series of large-deviation probabilities for sums of independent equally distributed random variables |
| title_alt | Сходимость рядов из вероятностей больших уклонений сумм независимых одинаково распределенных случайных величин |
| title_full | Convergence of the series of large-deviation probabilities for sums of independent equally distributed random variables |
| title_fullStr | Convergence of the series of large-deviation probabilities for sums of independent equally distributed random variables |
| title_full_unstemmed | Convergence of the series of large-deviation probabilities for sums of independent equally distributed random variables |
| title_short | Convergence of the series of large-deviation probabilities for sums of independent equally distributed random variables |
| title_sort | convergence of the series of large-deviation probabilities for sums of independent equally distributed random variables |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5866 |
| work_keys_str_mv | AT klesovoi convergenceoftheseriesoflargedeviationprobabilitiesforsumsofindependentequallydistributedrandomvariables AT klesovoi convergenceoftheseriesoflargedeviationprobabilitiesforsumsofindependentequallydistributedrandomvariables AT klesovoi convergenceoftheseriesoflargedeviationprobabilitiesforsumsofindependentequallydistributedrandomvariables AT klesovoi shodimostʹrâdovizveroâtnostejbolʹšihuklonenijsummnezavisimyhodinakovoraspredelennyhslučajnyhveličin AT klesovoi shodimostʹrâdovizveroâtnostejbolʹšihuklonenijsummnezavisimyhodinakovoraspredelennyhslučajnyhveličin AT klesovoi shodimostʹrâdovizveroâtnostejbolʹšihuklonenijsummnezavisimyhodinakovoraspredelennyhslučajnyhveličin |