独立随机序列加权和的强收敛性

STRONG CONVERGENCE OF WEIGHTED SUMS FOR INDPENDENT RANDOM VARIABLE SEQUENCE

本文研究独立随机变量序列加权和的强收敛性,利用截尾法和Borel-Cantelli引理,证明了加权系数ank为列阵情形的强收敛性,在一般双下标加权系数的加权部分和的强收敛性,并对Jamison型加权部分和情形证明了其强收敛的充要条件,推广了Chow与Teicher(1971)[3]的相应结果.

The main purpose of this paper is to study the strong convergence for the weighted partial sums of independent random variable sequence. By the method of truncation and Borel-Cantelli Lemma, we prove the strong convergence for the weighted partial sums in the case where the weighted coefficients αnk are array of real numbers, the strong convergence for the general double index weighted partial sums, the sufficient and necessary conditions of the strong convergence for the Jamison type weighted partial sums, which extends the corresponding result of Chow and Teicher（1971）[3].