Complete Convergence for Weighted Sums of a Class of Random Variables

被引：4

作者：

Deng, Xin ^{[1
]}

Ge, Meimei ^{[1
]}

Wang, Xuejun ^{[1
]}

Liu, Yanfang ^{[1
]}

Zhou, Yu ^{[1
]}

机构：

[1] Anhui Univ, Sch Math Sci, Hefei 230601, Peoples R China

来源：

FILOMAT | 2014年 / 28卷 / 03期

基金：

中国国家自然科学基金;

关键词：

complete convergence; weighted sums; Rosenthal type inequality; STATIONARY MIXING SEQUENCES; MAXIMAL INEQUALITIES; STRONG LAW; RATES;

D O I：

10.2298/FIL1403509D

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let {a(ni), 1 <= i <= n, n >= 1} be an array of real numbers and {X-n, n >= 1} be a sequence of random variables satisfying the Rosenthal type inequality, which is stochastically dominated by a random variable X. Under mild conditions, we present some results on complete convergence for weighted sums Sigma(n)(i=1) a(ni)X(i) of random variables satisfying the Rosenthal type inequality. The results obtained in the paper generalize some known ones in the literatures.

引用

页码：509 / 522

页数：14

共 24 条

[1] Marcinkiewicz strong laws for linear statistics [J].

Bai, ZD ;

Cheng, PE .

STATISTICS & PROBABILITY LETTERS, 2000, 46 (02) :105-112

[2] CONVERGENCE RATES IN LAW OF LARGE NUMBERS [J].

BAUM, LE ;

KATZ, M .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1965, 120 (01) :108-&

[3] ON A THEOREM OF HSU AND ROBBINS [J].

ERDOS, P .

ANNALS OF MATHEMATICAL STATISTICS, 1949, 20 (02) :286-291

[4] COMPLETE CONVERGENCE AND THE LAW OF LARGE NUMBERS [J].

HSU, PL ;

ROBBINS, H .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1947, 33 (02) :25-31

[5] CONVERGENCE RATES AND R-QUICK VERSIONS OF STRONG LAW FOR STATIONARY MIXING SEQUENCES [J].

LAI, TL .

ANNALS OF PROBABILITY, 1977, 5 (05) :693-706

[6] CONVERGENCE-RATES OF THE STRONG LAW FOR STATIONARY MIXING SEQUENCES [J].

PELIGRAD, M .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1985, 70 (02) :307-314

[7]

Shao Q.M., 1988, Acta Math. Sinica Chin. Ser, V31, P736

[8] MAXIMAL INEQUALITIES FOR PARTIAL-SUMS OF RHO-MIXING SEQUENCES [J].

SHAO, QM .

ANNALS OF PROBABILITY, 1995, 23 (02) :948-965

[9] A comparison theorem on moment inequalities between negatively associated and independent random variables [J].

Shao, QM .

JOURNAL OF THEORETICAL PROBABILITY, 2000, 13 (02) :343-356

[10]

Shen A.T., 2013, ABSTR APPL AN, V2013

← 1 2 3 →