On fluctuations of sums of random variables
On fluctuations of sums of random variables
复制标题
关于随机变量之和的波动
DOI：
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发表时间：
1955
期刊：
影响因子：
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通讯作者：
L. J. Cote
中科院分区：
文献类型：
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作者：
L. J. Cote
介绍。这些结果是Chung [i]定理对值C的限制分布C的限制分布，C，通过一系列独立随机变量的连续部分总和以及Chung和Erdos的定理[3] [3]在此类总和的下限上。这些定理中的两个涉及独立，等级的随机变量的情况，其分布具有绝对连续的组件（案例A）。其他是用于二项式变体（情况B）。我们将案例A的结果扩展到独立随机变量的总和，其分布不需要相同，案例B的总和到晶格类型的独立和等分分配随机变量的总和。令{x}为独立随机变量的序列，其c.d.f.的{fn（x）}不必是相同的。我们使用通常的符号：
Introduction. These results are generalizations of a theorem of Chung [I ] on the limiting distribution of the number of crossings of a value, c, by the successive partial sums of a sequence of independent random variables, and of theorems by Chung and Erdos [3 ] on the lower limits of such sums. Two of these theorems concern the case of independent, equidistributed random variables whose distributions have an absolutely continuous component (Case A). The others are for binomial variates (Case B). We extend the results of Case A to sums of independent random variables whose distributions need not be the same, and those of Case B to sums of independent and equidistributed random variables of the lattice type. Let {X } be a sequence of independent random variables whose c.d.f.'s, { Fn(x) }, need not be the same. We use the usual notations: