On the Strong Limit Theorems for Double Arrays of Blockwise M-dependent Random Variables

被引：18

作者：

Stadtmueller, Ulrich ^{[1
]}

Le Van Thanh ^{[2
]}

机构：

[1] Univ Ulm, Dept Number & Probabil Theory, D-89069 Ulm, Germany

[2] Vinh Univ, Dept Math, Nghe An 42118, Vietnam

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2011年 / 27卷 / 10期

关键词：

Blockwise M-dependent random variables; strong law of large numbers; double arrays of random variables; almost sure convergence; ORTHOGONAL RANDOM ELEMENTS; LARGE NUMBERS; STRONG LAWS; DIMENSIONAL ARRAYS; CONVERGENCE-RATES; BANACH-SPACES; SEQUENCES; SUMS;

D O I：

10.1007/s10114-011-0110-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a double array of blockwise M-dependent random variables {X-mn, m >= 1, n >= 1}, strong laws of large numbers are established for double sums Sigma(m)(i=1) Sigma(n)(j=1) X-ij, m >= 1, n >= 1. The main results are obtained for (i) random variables {X-mn, m >= 1, n >= 1} being non-identically distributed but satisfy a condition on the summability condition for the moments and (ii) random variables {X-mn, m >= 1, n >= 1} being stochastically dominated. The result in Case (i) generalizes the main result of Moricz et al. [J. Theoret. Probab., 21, 660-671 (2008)] from dyadic to arbitrary blocks, whereas the result in Case (ii) extends a result of Gut [ Ann. Probab., 6, 469-482 (1978)] to the bockwise M-dependent setting. The sharpness of the results is illustrated by some examples.

引用

页码：1923 / 1934

页数：12

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