论文标题
通过其Laplace-Stieltjes变换应用于分布的唯一性的两个积分变换的身份
An Identity for Two Integral Transforms Applied to the Uniqueness of a Distribution via its Laplace-Stieltjes Transform
论文作者
论文摘要
众所周知，非负随机变量（或随机矢量）的Laplace-Stieltjes唯一决定其分布函数。我们通过使用Muntz-Szasz定理以及分布函数的Laplace-Stieltjes和Laplace-Carson变换来扩展这种唯一性定理。据我们所知，后者首次出现。特别是，如果x和y是两个具有关节分布h的非负随机变量，则H可以以合适的一组其双变量Laplace-Stieltjes变换为特征。还研究了一般的高维情况。此外，Lerch对传统拉普拉斯变换的独特定理也扩展了。当基础分布具有单数零件时，该身份可用于简化拉普拉斯 - 斯泰尔杰斯变换的计算。最后，给出了一些示例，以通过唯一性定理说明表征结果。
It is well known that the Laplace-Stieltjes transform of a nonnegative random variable (or random vector) uniquely determines its distribution function. We extend this uniqueness theorem by using the Muntz-Szasz Theorem and the identity for the Laplace-Stieltjes and Laplace-Carson transforms of a distribution function. The latter appears for the first time to the best of our knowledge. In particular, if X and Y are two nonnegative random variables with joint distribution H, then H can be characterized by a suitable set of countably many values of its bivariate Laplace-Stieltjes transform. The general high-dimensional case is also investigated. Besides, Lerch's uniqueness theorem for conventional Laplace transforms is extended as well. The identity can be used to simplify the calculation of Laplace-Stieltjes transforms when the underlying distributions have singular parts. Finally, some examples are given to illustrate the characterization results via the uniqueness theorem.
