连续随机变量的舍入与振荡渐近性
Rounding of continuous random variables and oscillatory asymptotics
摘要：
研究了整数随机变量$\lfloor X+α\rfloor$的特征函数和特征矩，其中$X$是连续随机变量。这些结果可以看作是Sheppard修正的精确形式。这种类型的舍入变量经常作为整数值随机变量序列的子序列极限出现。这导致了这些变量的渐近性中的振荡项，这是经常观察到的，例如在几个算法的分析中。我们给出了一些例子，包括应用到尝试，数字搜索树和帕特里夏尝试。
英文摘要：
We study the characteristic function and moments of the integer-valued random variable $\lfloor X+α\rfloor$, where $X$ is a continuous random variables. The results can be regarded as exact versions of Sheppard's correction. Rounded variables of this type often occur as subsequence limits of sequences of integer-valued random variables. This leads to oscillatory terms in asymptotics for these variables, something that has often been observed, for example in the analysis of several algorithms. We give some examples, including applications to tries, digital search trees and Patricia tries.
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