On One Sufficient Condition for the Validity of the Strong Law of Large Numbers for Martingales
We prove a theorem on the strong law of large numbers for martingales. The existence of higher moments is not assumed. From the theorem proved, we deduce numerous well-known results on the strong law of large numbers both for martingales and for sequences of sums of independent random variables.
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| Datum: | 2000 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2000
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4542 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510679765614592 |
|---|---|
| author | Koval, V. A. Коваль, В. А. Коваль, В. А. |
| author_facet | Koval, V. A. Коваль, В. А. Коваль, В. А. |
| author_sort | Koval, V. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:30:59Z |
| description | We prove a theorem on the strong law of large numbers for martingales. The existence of higher moments is not assumed. From the theorem proved, we deduce numerous well-known results on the strong law of large numbers both for martingales and for sequences of sums of independent random variables. |
| first_indexed | 2026-03-24T03:00:50Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4542 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:00:50Z |
| publishDate | 2000 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/44/b9dd68e65ac2052bf8c7b33ac5087744.pdf |
| spelling | umjimathkievua-article-45422020-03-18T20:30:59Z On One Sufficient Condition for the Validity of the Strong Law of Large Numbers for Martingales Об одном достаточном условии выполнения усиленного закона больших чисел для мартингалов Koval, V. A. Коваль, В. А. Коваль, В. А. We prove a theorem on the strong law of large numbers for martingales. The existence of higher moments is not assumed. From the theorem proved, we deduce numerous well-known results on the strong law of large numbers both for martingales and for sequences of sums of independent random variables. Доведено теорему про підсилений закон великих чисел для мартгаїгалів. При цьому не припускається існування моментів, вищих за перший. Із доведеної теореми виводиться ряд відомих результатів про підсилений закон великих чисел як для мартингалів, так і для послідовностей сум незалежних випадкових величин. Institute of Mathematics, NAS of Ukraine 2000-10-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4542 Ukrains’kyi Matematychnyi Zhurnal; Vol. 52 No. 10 (2000); 1357-1362 Український математичний журнал; Том 52 № 10 (2000); 1357-1362 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4542/5788 https://umj.imath.kiev.ua/index.php/umj/article/view/4542/5789 Copyright (c) 2000 Koval V. A. |
| spellingShingle | Koval, V. A. Коваль, В. А. Коваль, В. А. On One Sufficient Condition for the Validity of the Strong Law of Large Numbers for Martingales |
| title | On One Sufficient Condition for the Validity of the Strong Law of Large Numbers for Martingales |
| title_alt | Об одном достаточном условии выполнения усиленного закона больших
чисел для мартингалов |
| title_full | On One Sufficient Condition for the Validity of the Strong Law of Large Numbers for Martingales |
| title_fullStr | On One Sufficient Condition for the Validity of the Strong Law of Large Numbers for Martingales |
| title_full_unstemmed | On One Sufficient Condition for the Validity of the Strong Law of Large Numbers for Martingales |
| title_short | On One Sufficient Condition for the Validity of the Strong Law of Large Numbers for Martingales |
| title_sort | on one sufficient condition for the validity of the strong law of large numbers for martingales |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4542 |
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