关于任意随机序列加权和的强收敛性
On Almost Sure Convergence for Weighted Sums of Arbitrarily Dependent Random Sequences

DOI: 10.12677/PM.2016.61004, PP. 23-29

Keywords: 随机控制，加权和，强大数定律
Randomized Controlled, Weighted Sums, Strong Law of Large Numbers

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Abstract:

设{X_n}_n=1^∞ ？是一列任意相依随机变量序列，且{X_n}_n=1^∞ ？？ X。本文利用Borel-Cantelli引理与概率论极限理论中的纯分析方法，讨论一类相依随机变量序列的强收敛性，得到了任意相依随机变量序列加权和的强大数定律普遍成立的若干充分条件，并推广了已有的结果。
Let {X_n}_n=1^∞ ？be a sequence of arbitrarily dependent random variables with {X_n}_n=1^∞ ？？ X. In this 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 sufficient conditions on strong law of large numbers for weighted sums of arbitrarily random sequences are also obtained. Some classical results are generalized.

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