On strong law of large numbers and growth rate for a class of random variables

被引：3

作者：

Shen, Yan ^{[1
]}

Yang, Jie ^{[1
]}

Hu, Shuhe ^{[1
]}

机构：

[1] Anhui Univ, Sch Math Sci, Hefei 230039, Peoples R China

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2013年

基金：

中国国家自然科学基金;

关键词：

strong law of large numbers; weighted sums; with exponent 2; DEPENDENT RANDOM-VARIABLES; WEIGHTED SUMS; SURE CONVERGENCE; GENERAL-APPROACH; STABILITY;

D O I：

10.1186/1029-242X-2013-563

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the strong law of large numbers for a class of random variables satisfying the maximal moment inequality with exponent 2. Our results embrace the Kolmogorov strong law of large numbers and the Marcinkiewicz strong law of large numbers for this class of random variables. In addition, strong growth rate for weighted sums of this class of random variables is presented.

引用

页数：11

共 23 条

[1] ON THE STRONG LAW OF LARGE NUMBERS FOR NORMED WEIGHTED SUMS OF IID RANDOM-VARIABLES [J].

ADLER, A ;

ROSALSKY, A .

STOCHASTIC ANALYSIS AND APPLICATIONS, 1987, 5 (04) :467-483

[2] ALMOST CERTAIN SUMMABILITY OF INDEPENDENT, IDENTICALLY DISTRIBUTED RANDOM VARIABLES [J].

CHOW, YS ;

TEICHER, H .

ANNALS OF MATHEMATICAL STATISTICS, 1971, 42 (01) :401-&

[3] A general approach to the strong law of large numbers [J].

Fazekas, I ;

Klesov, O .

THEORY OF PROBABILITY AND ITS APPLICATIONS, 2000, 45 (03) :436-449

[4] STABILITY OF RANDOM-VARIABLES AND ITERATED LOGARITHM LAWS FOR MARTINGALES AND QUADRATIC-FORMS [J].

FERNHOLZ, LT ;

TEICHER, H .

ANNALS OF PROBABILITY, 1980, 8 (04) :765-774

[5] A general approach rate to the strong law of large numbers [J].

Hu, SH ;

Ming, H .

STATISTICS & PROBABILITY LETTERS, 2006, 76 (08) :843-851

[6]

[胡舒合 Hu Shuhe], 2003, [数学学报, Acta Mathematica Sinica], V46, P1123

[7] The Hajek-Renyi-type inequality for associated random variables [J].

Hu Shuhe ;

Wang Xuejun ;

Yang Wenzhi ;

Zhao Ting .

STATISTICS & PROBABILITY LETTERS, 2009, 79 (07) :884-888

[8]

Jamison B., 1965, Z WAHRSCHEINLICHKEIT, V4, P40, DOI [10.1007/BF00535481, DOI 10.1007/BF00535481]

[9] A NOTE ON THE ALMOST SURE CONVERGENCE OF SUMS OF NEGATIVELY DEPENDENT RANDOM-VARIABLES [J].

MATULA, P .

STATISTICS & PROBABILITY LETTERS, 1992, 15 (03) :209-213

[10]

RAO M. M., 1987, Measure theory and integration

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