Weak laws of large numbers for arrays under a condition of uniform integrability

被引：29

作者：

Sung, Soo Hak ^{[1
]}

Lisawadi, Supranee ^{[2
]}

Volodin, Andrei ^{[2
]}

机构：

[1] Pai Chai Univ, Dept Appl Math, Taejon 302735, South Korea

[2] Univ Regina, Dept Math & Stat, Regina, SK S4S 0A2, Canada

来源：

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2008年 / 45卷 / 01期

关键词：

uniform integrability; weak law of large numbers; r-mean convergence; convergence in probability; martingale difference sequence; negative association; negative dependence;

D O I：

10.4134/JKMS.2008.45.1.289

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For an array of dependent random variables satisfying a new notion of uniform integrability, weak laws of large numbers are obtained. Our results extend and sharpen the known results in the literature.

引用

页码：289 / 300

页数：12

共 14 条

[1] Mean convergence theorems and weak laws of large numbers for weighted sums of random variables under a condition of weighted integrability
Cabrera, MO
Volodin, AI
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 305 (02) : 644 - 658
[2] CHANDRA TK, 1989, SANKHYA SER A, V51, P309
[3] Cesaro α-Integrability and laws of large numbers I
Chandra, TK
Goswami, A
[J]. JOURNAL OF THEORETICAL PROBABILITY, 2003, 16 (03) : 655 - 669
[4] AN ELEMENTARY PROOF OF THE STRONG LAW OF LARGE NUMBERS
ETEMADI, N
[J]. ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1981, 55 (01): : 119 - 122
[5] THE WEAK LAW OF LARGE NUMBERS FOR ARRAYS
GUT, A
[J]. STATISTICS & PROBABILITY LETTERS, 1992, 14 (01) : 49 - 52
[6] HONG DH, 1995, STAT PROBABIL LETT, V22, P55
[7] NEGATIVE ASSOCIATION OF RANDOM-VARIABLES, WITH APPLICATIONS
JOAGDEV, K
PROSCHAN, F
[J]. ANNALS OF STATISTICS, 1983, 11 (01) : 286 - 295
[8] [Круглов В. М Kruglov V.M.], 2006, [Теория вероятностей и ее применения, Theory of Probability and its Applications, Teoriya veroyatnostei i ee primeneniya], V51, P382
[9] LAWS OF LARGE NUMBERS FOR PAIRWISE INDEPENDENT UNIFORMLY INTEGRABLE RANDOM-VARIABLES
LANDERS, D
ROGGE, L
[J]. MATHEMATISCHE NACHRICHTEN, 1987, 130 : 189 - 192
[10] Li DL, 2006, BULL INST MATH ACAD, V1, P281

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