Best Possible Sufficient Conditions for Strong Law of Large Numbers for Multi-Indexed Orthogonal Random Elements
It will be shown and induced that the d-dimensional indices in the Banach spaces version conditions ∑n(E‖Xn‖p/|nα|p)<∞ are sufficient to yield limmin1≤j≤d(nj)→∞(1/|nα|)∑k≤n∏j=1d(1−(kj−1)/nj)Xk=0 a.s. for arrays of James-type orthogonal random elements. Particularly, it will be shown also that the...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/86909 |
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| _version_ | 1832551141021319168 |
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| author | Kuo-Liang Su |
| author_facet | Kuo-Liang Su |
| author_sort | Kuo-Liang Su |
| collection | DOAJ |
| description | It will be shown and induced that the d-dimensional indices in the Banach spaces version conditions ∑n(E‖Xn‖p/|nα|p)<∞ are sufficient to yield limmin1≤j≤d(nj)→∞(1/|nα|)∑k≤n∏j=1d(1−(kj−1)/nj)Xk=0 a.s. for arrays of James-type orthogonal random elements. Particularly, it will be shown also that there are the best possible sufficient conditions for multi-indexed independent real-valued random variables. |
| format | Article |
| id | doaj-art-bd59b6a3456f4b458a923ced08e6da63 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-bd59b6a3456f4b458a923ced08e6da632025-02-03T06:04:58ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/8690986909Best Possible Sufficient Conditions for Strong Law of Large Numbers for Multi-Indexed Orthogonal Random ElementsKuo-Liang Su0Department of Business, National Open University, Lu Chow 247, Taipei, TaiwanIt will be shown and induced that the d-dimensional indices in the Banach spaces version conditions ∑n(E‖Xn‖p/|nα|p)<∞ are sufficient to yield limmin1≤j≤d(nj)→∞(1/|nα|)∑k≤n∏j=1d(1−(kj−1)/nj)Xk=0 a.s. for arrays of James-type orthogonal random elements. Particularly, it will be shown also that there are the best possible sufficient conditions for multi-indexed independent real-valued random variables.http://dx.doi.org/10.1155/2007/86909 |
| spellingShingle | Kuo-Liang Su Best Possible Sufficient Conditions for Strong Law of Large Numbers for Multi-Indexed Orthogonal Random Elements International Journal of Mathematics and Mathematical Sciences |
| title | Best Possible Sufficient Conditions for Strong Law of Large Numbers for Multi-Indexed Orthogonal Random Elements |
| title_full | Best Possible Sufficient Conditions for Strong Law of Large Numbers for Multi-Indexed Orthogonal Random Elements |
| title_fullStr | Best Possible Sufficient Conditions for Strong Law of Large Numbers for Multi-Indexed Orthogonal Random Elements |
| title_full_unstemmed | Best Possible Sufficient Conditions for Strong Law of Large Numbers for Multi-Indexed Orthogonal Random Elements |
| title_short | Best Possible Sufficient Conditions for Strong Law of Large Numbers for Multi-Indexed Orthogonal Random Elements |
| title_sort | best possible sufficient conditions for strong law of large numbers for multi indexed orthogonal random elements |
| url | http://dx.doi.org/10.1155/2007/86909 |
| work_keys_str_mv | AT kuoliangsu bestpossiblesufficientconditionsforstronglawoflargenumbersformultiindexedorthogonalrandomelements |