随机变量序列完全收敛的等价及充分条件
Equivalent and Sufficient Conditions of Complete Convergence of Random Variables Sequence
DOI: 10.12677/AAM.2018.76080, PDF,   
作者: 袁代林：西南交通大学数学学院，四川 成都
关键词: 完全收敛；等价条件；充分条件；Complete Convergence； Equivalent Condition； Sufficient Condition
摘要: 在随机变量序列收敛性的判断中，考虑了单调递减趋于0的实数数列，得到了随机变量序列完全收敛的等价条件和两个充分条件。同时研究了序列的几乎必然收敛和依概率收敛，用例子说明了这些条件之间的相互关系。
Abstract: The equivalent condition and two sufficient conditions of complete convergence were obtained based on a monotone decreasing real sequence converging to 0, when the convergence of a random variables sequence was considered. At the same time, the related issues about almost sure convergence and convergence in probability were researched. The interrelations of these conditions were obtained and exemplified.
文章引用：袁代林. 随机变量序列完全收敛的等价及充分条件[J]. 应用数学进展, 2018, 7(6): 673-679. https://doi.org/10.12677/AAM.2018.76080

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