Equivalent conditions of complete moment convergence of weighted sums for ρ*-mixing sequence of random variables

被引：25

作者：

Guo, Mingle ^{[1
]}

Zhu, Dongjin ^{[1
]}

机构：

[1] Anhui Normal Univ, Sch Math & Comp Sci, Wuhu 241000, Peoples R China

来源：

STATISTICS & PROBABILITY LETTERS | 2013年 / 83卷 / 01期

基金：

中国国家自然科学基金;

关键词：

rho*-mixing sequence of random variables; Weighted sums; Complete convergence; Complete moment convergence; DEPENDENT RANDOM-VARIABLES; SURE CONVERGENCE;

D O I：

10.1016/j.spl.2012.08.015

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, the complete moment convergence of weighted sums for rho*-mixing sequence of random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete moment convergence of weighted sums for rho*-mixing sequence of random variables are established. These results promote and improve the corresponding results obtained by Li et al. (1995) and Gut (1993) from i.i.d. to rho*-mixing setting. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：13 / 20

页数：8

共 10 条

[1]

[Anonymous], 2008, STAT PROBABIL LETT

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

BAUM, LE ;

KATZ, M .

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

[3]

Bradley R.C., 1992, J THEOR PROBAB, V5, P355, DOI [10.1007/BF01046741, DOI 10.1007/BF01046741]

[4] MOMENT CONDITIONS FOR ALMOST SURE CONVERGENCE OF WEAKLY CORRELATED RANDOM-VARIABLES [J].

BRYC, W ;

SMOLENSKI, W .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 119 (02) :629-635

[5] COMPLETE CONVERGENCE AND CESARO SUMMATION FOR IID RANDOM-VARIABLES [J].

GUT, A .

PROBABILITY THEORY AND RELATED FIELDS, 1993, 97 (1-2) :169-178

[6] 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

[7] COMPLETE CONVERGENCE AND ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM-VARIABLES [J].

LI, DL ;

RAO, MB ;

JIANG, TF ;

WANG, XC .

JOURNAL OF THEORETICAL PROBABILITY, 1995, 8 (01) :49-76

[8] Complete convergence for weighted sums of negatively associated random variables [J].

Liang, HY .

STATISTICS & PROBABILITY LETTERS, 2000, 48 (04) :317-325

[9] Almost-sure results for a class of dependent random variables [J].

Peligrad, M ;

Gut, A .

JOURNAL OF THEORETICAL PROBABILITY, 1999, 12 (01) :87-104

[10] Maximum of partial sums and an invariance principle for a class of weak dependent random variables [J].

Peligrad, M .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 126 (04) :1181-1189

← 1 →