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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Bibliographic Details
Published inChinese annals of mathematics. Serie B Vol. 21; no. 1; pp. 83 - 88
Main Author Liang, Hanying
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.01.2000
Department of Applied Mathematics, Tongji University, Shanghai 200092, China
Subjects
B-值随机变量
Convergence
Equivalence
Probability theory
全收敛
独立随机变量
B-valued random element
Complete convergence
Law of large number
Equivalence
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ISSN0252-9599
1860-6261
DOI10.1007/BF02731962

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Summary: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.
Bibliography:31-1329/O1
O211.4
ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0252-9599
1860-6261
DOI:10.1007/BF02731962