On the Strong Law of Large Numbers for Sequences of Dependent Random Variables with Finite Second Moments

被引：0
|
作者：
Korchevsky V.M. [1 ]
机构：
[1] St. Petersburg State University of Aerospace Instrumentation, St. Petersburg
来源：
Journal of Mathematical Sciences | 2015年 / 206卷 / 2期
关键词：
Satisfying Condition; Independent Random Variable; Nondecreasing Function; Dependent Random Variable; Nonnegative Random Variable;
D O I：
10.1007/s10958-015-2303-y
中图分类号：
学科分类号：
摘要：
New sufficient conditions of a.s. convergence of the series (Formula Presented) and new sufficient conditions for the applicability of the strong law of large numbers are established for a sequence of dependent random variables {Xn}n = 1∞ with finite second moments. These results are generalizations of the well-known theorems on a.s. convergence of the series of orthogonal random variables and on the strong law of large numbers for orthogonal random variables (Men’shov–Rademacher and Petrov’s theorems). It is shown that some of the results obtained are optimal. © 2015, Springer Science+Business Media New York.
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页码：197 / 206
页数：9
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