关于任意随机序列加权和的强收敛性.pdfVIP

Pure Mathematics 理论数学, 2016, 6(1), 23-29 Published Online January 2016 in Hans. /journal/pm /10.12677/pm.2016.61004 On Almost Sure Convergence for Weighted Sums of Arbitrarily Dependent Random Sequences Qiong Wang, Ying Cui, Aihua Fan* School of Mathematics Physics Science and Engineering, Anhui University of Technology, Ma’anshan Anhui th th nd Received: Dec. 17 , 2015; accepted: Jan. 19 , 2016; published: Jan. 22 , 2016 Copyright © 2016 by authors and Hans Publishers Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). /licenses/by/4.0/ Abstract ∞ ∞ Let X be a sequence of arbitrarily dependent random variables with X X . In this { } { } n n 1 n n 1 paper, by using the Borel-Cantelli lemma and the pure analysis method in probability limit theory, some strong convergence of a class of dependent random variables is discussed and some suffi- cient conditions on strong law of large numbers for weighted sums of arbitrarily random se- quences are also obtained. Some classical results are generalized. Keywords Randomized Controlled, Weighted Sums, Strong Law of Large Numbers 关于任意随机序列加权和的强收敛性 汪 琼，崔 影，范爱华* 安徽工业大学数理科学与工程学院，安徽 马鞍山 收稿日期：2015年12月17 日；录用日期：2016年1月19 日；发布日期：2016年1月22 日 *通讯作者。 文章引用: 汪琼, 崔影, 范爱华. 关于任意随机序列加权和的强收敛性[J]. 理论数学, 2016, 6(1): 23-29. /10.12677/pm.2016.61004 汪琼 等 摘 要 ∞