EQUIVALENCE OF COMPLETE CONVERGENCE AND LAW OF LARGE NUMBERS FOR B-VALUED RANDOM ELEMENTS
Under some conditions on probability, this note discusses the equivalence between the complete convergence and the law of large number for B-valued independent random elements. The results of [10] become a simple corollary of the results here. At the same time, the author uses them to investigate th...
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| Published in | Chinese annals of mathematics. Serie B Vol. 21; no. 1; pp. 83 - 88 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
Springer Nature B.V
01.01.2000
Department of Applied Mathematics, Tongji University, Shanghai 200092, China |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0252-9599 1860-6261 |
| DOI | 10.1007/BF02731962 |
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| Abstract | Under some conditions on probability, this note discusses the equivalence between the complete convergence and the law of large number for B-valued independent random elements. The results of [10] become a simple corollary of the results here. At the same time, the author uses them to investigate the equivalence of strong and weak law of large numbers, and there exists an example to show that the conditions on probability are weaker. |
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| AbstractList | O211.4; Under some conditions on probability, this note discusses the equivalence between the complete convergence and the law of large number for B-valued independent random elements. The results of [10] become a simple corollary of the results here. At the same time, the author uses them to investigate the equivalence of strong and weak law of large numbers, and there exists an example to show that the conditions on probability are weaker. Under some conditions on probability, this note discusses the equivalence between the complete convergence and the law of large number for B-valued independent random elements. The results of [10] become a simple corollary of the results here. At the same time, the author uses them to investigate the equivalence of strong and weak law of large numbers, and there exists an example to show that the conditions on probability are weaker. |
| Author | LIANGHANYING |
| AuthorAffiliation | DepartmentofAppliedMathematics,TongjiUniversity,Shanghai200092,China. |
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| Cites_doi | 10.1080/07362999308809305 10.1214/aop/1176994517 10.1137/1126062 10.1007/BF00534961 |
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| Copyright | Shanghai Scientific & Technological Literature Publishing House 1980. Copyright © Wanfang Data Co. Ltd. All Rights Reserved. |
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| Keywords | B-valued random element Complete convergence Law of large number Equivalence |
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| References | T A Azalarov (11_CR1) 1981; 26 11_CR6 11_CR8 Z Q Wu (11_CR9) 1987; 3 H Y Liang (11_CR5) 1997; 40 A de Acosta (11_CR3) 1981; 9 X Y Yang (11_CR10) 1993; 36 Z D Bai (11_CR2) 1985; 28 N C Jain (11_CR4) 1975; 33 X C Wang (11_CR7) 1993; 11 |
| References_xml | – volume: 3 start-page: 228 issue: 2 year: 1987 ident: 11_CR9 publication-title: Northeastern Math. J. – volume: 11 start-page: 115 issue: 1 year: 1993 ident: 11_CR7 publication-title: Stochatic Anal. Appl. doi: 10.1080/07362999308809305 – volume: 36 start-page: 817 issue: 6 year: 1993 ident: 11_CR10 publication-title: Acta Math. Sinica – volume: 40 start-page: 449 year: 1997 ident: 11_CR5 publication-title: Acta Math. Sinica – ident: 11_CR6 – volume: 9 start-page: 157 year: 1981 ident: 11_CR3 publication-title: Ann. Probab. doi: 10.1214/aop/1176994517 – volume: 26 start-page: 573 year: 1981 ident: 11_CR1 publication-title: Probab. Theor. Appl. doi: 10.1137/1126062 – volume: 33 start-page: 155 year: 1975 ident: 11_CR4 publication-title: Z. Wahr. Verw. Gebiete doi: 10.1007/BF00534961 – volume: 28 start-page: 1261 year: 1985 ident: 11_CR2 publication-title: Sci. Sinica (Ser.A) – ident: 11_CR8 |
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| Snippet | Under some conditions on probability, this note discusses the equivalence between the complete convergence and the law of large number for B-valued independent... O211.4; Under some conditions on probability, this note discusses the equivalence between the complete convergence and the law of large number for B-valued... |
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| SubjectTerms | B-值随机变量 Convergence Equivalence Probability theory 全收敛 独立随机变量 |
| Title | EQUIVALENCE OF COMPLETE CONVERGENCE AND LAW OF LARGE NUMBERS FOR B-VALUED RANDOM ELEMENTS |
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