﻿ 两两NQD列的若干收敛性质 Some Convergence Properties of Pairwise NQD Random Sequences

Vol.05 No.01(2016), Article ID:17035,7 pages
10.12677/AAM.2016.51019

Some Convergence Properties of Pairwise NQD Random Sequences

Ying Lin1, Jianhua Shi2

1Department of Mathematics, Ningde Normal University, Ningde Fujian

2School of Mathematics and Statistics, Minnan Normal University, Zhangzhou Fujian

Received: Feb. 2nd, 2016; accepted: Feb. 22nd, 2016; published: Feb. 29th, 2016

ABSTRACT

In this paper, Lr convergence and weak law of large numbers for the weighted sums of rowwise and pairwise NQD arrays are studied, moreover, a theorem of complete convergence for the weighted sums of pairwise NQD sequences is obtained.

Keywords:Pairwise NQD Random Sequences, Cesáro Uniform Integrability, Convergence Property

1宁德师范学院数学系，福建 宁德

2闽南师范大学数学与统计学院，福建 漳州

1. 引言与引理

1)；2)为常数。

；3) 如同为非降(或非增)函数，则仍为NQD的。

，则有

2. 两两NQD列的Lr收敛性及弱大数定律

，则均为的不降函数，由引理1知仍为两两NQD的。由引理2，有

1)阶Cesáro一致可积的；2)是行为两两NQD的零均值阵列，且为2阶Cesáro一致可积的，则。更有如下形式的弱大数定律成立：

-Toeplitz矩阵，又，故由定理1立即知定理2的(2)成立。

，则对，有

3. 两两NQD列加权和的完全收敛性

，则对任意的，有

Some Convergence Properties of Pairwise NQD Random Sequences[J]. 应用数学进展, 2016, 05(01): 143-149. http://dx.doi.org/10.12677/AAM.2016.51019

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