论文标题
紧凑型代数组的独立样品的随机变量分布分布的收敛性
Convergence in distribution of the product of random variables from an independent sample on a compact algebraic group
论文作者
论文摘要
随着样本量增加，在紧凑的代数组上，分布中的独立随机样品的元素的乘积等效条件。也就是说，如果具有这种分布的随机变量不属于与任何非平凡的coset的单位概率，则存在于母体分布的支撑，并且在其标准器的代数亚组上不属于单位概率；否则，它不存在。
An equivalent condition for the product of elements of an independent random sample on a compact algebraic group converging in distribution to some random variable as the sample size increases is obtained. Namely, a limit distribution exists and is uniform on the support of the parent distribution if a random variable with such a distribution does not belong with the unit probability to any non-trivial coset over an algebraic subgroup that lies in its normalizer; otherwise, it does not exist.
