Complete Convergence and Complete Moment Convergence for Martingale Difference Sequence

被引：47

作者：

Wang, Xue Jun ^{[1
]}

Hu, Shu He ^{[1
]}

机构：

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

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2014年 / 30卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Martingale difference sequence; complete convergence; complete moment convergence; Baum-Katz-type theorem; LARGE NUMBERS; LAW;

D O I：

10.1007/s10114-013-2243-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the paper, we investigate the complete convergence and complete moment convergence for the maximal partial sum of martingale difference sequence. Especially, we get the Baum-Katz-type Theorem and Hsu-Robbins-type Theorem for martingale difference sequence. As an application, a strong law of large numbers for martingale difference sequence is obtained.

引用

页码：119 / 132

页数：14

共 13 条

[1]

BAI ZD, 1985, SCI SIN A-MATH P A T, V28, P1261

[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 of martingale arrays [J].

Ghosal, S ;

Chandra, TK .

JOURNAL OF THEORETICAL PROBABILITY, 1998, 11 (03) :621-631

[5]

Hall P., 1980, Martingale Limit Theory and Its Application

[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] Baum-Katz-Nagaev type results for martingales [J].

Stoica, George .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 336 (02) :1489-1492

[8] A note on the rate of convergence in the strong law of large numbers for martingales [J].

Stoica, George .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 381 (02) :910-913

[9] Moment Inequalities and Complete Moment Convergence [J].

Sung, Soo Hak .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2009,

[10]

Wu, 2006, LIMIT THEOREM PROBAB

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