On the strong law of large numbers for d-dimensional arrays of random variables

被引：0

作者：

Thanh, Le Van ^{[1
]}

机构：

[1] Vinh Univ, Dept Math, Nghe An 42118, Vietnam

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2007年 / 12卷

关键词：

strong law of large number; almost sure convergence; d-dimensional arrays of random variables;

D O I：

暂无

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper, we provide a necessary and sufficient condition for general d-dimensional arrays of random variables to satisfy strong law of large numbers. Then, we apply the result to obtain some strong laws of large numbers for d-dimensional arrays of blockwise independent and blockwise orthogonal random variables.

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页码：434 / 441

页数：8

相关论文

共 12 条

[1] Prokhorov blocks and strong law of large numbers under rearrangements [J].

Chobanyan, S ;

Levental, S ;

Mandrekar, V .

JOURNAL OF THEORETICAL PROBABILITY, 2004, 17 (03) :647-672

[2]

Chow Y.S., 1997, Springer Texts in Statistics

[3] NOTE ON SOME STRONG LAWS OF LARGE NUMBERS [J].

CHUNG, KL .

AMERICAN JOURNAL OF MATHEMATICS, 1947, 69 (01) :189-192

[4]

Gaposhkin V F, 1995, THEOR PROBAB APPL, V39, P667

[5] MARCINKIEWICZ LAWS AND CONVERGENCE RATES IN LAW OF LARGE NUMBERS FOR RANDOM-VARIABLES WITH MULTIDIMENSIONAL INDEXES [J].

GUT, A .

ANNALS OF PROBABILITY, 1978, 6 (03) :469-482

[6] STRONG LAWS OF LARGE NUMBERS FOR FIELDS OF BANACH-SPACE VALUED RANDOM-VARIABLES [J].

MIKOSCH, T ;

NORVAISA, R .

PROBABILITY THEORY AND RELATED FIELDS, 1987, 74 (02) :241-253

[7] STRONG LIMIT-THEOREMS FOR BLOCKWISE META-DEPENDENT AND BLOCKWISE QUASIORTHOGONAL SEQUENCES OF RANDOM-VARIABLES [J].

MORICZ, F .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 101 (04) :709-715

[8]

MORICZ F, 1977, ACTA SCI MATH, V39, P353

[9] STRONG LIMIT-THEOREMS FOR QUASI-ORTHOGONAL RANDOM-FIELDS [J].

MORICZ, F .

JOURNAL OF MULTIVARIATE ANALYSIS, 1989, 30 (02) :255-278

[10] STRONG LAWS OF LARGE NUMBERS FOR R-DIMENSIONAL ARRAYS OF RANDOM-VARIABLES [J].

SMYTHE, RT .

ANNALS OF PROBABILITY, 1973, 1 (01) :164-170