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math.PR2020★ 2 cited
An Identity for Two Integral Transforms Applied to the Uniqueness of a Distribution via its Laplace-Stieltjes Transform
Gwo Dong Lin, Xiaoling Dou
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 t…
math.PR2020
Characterization of Probability Distributions via Functional Equations of Power-Mixture Type
Chin-Yuan Hu, Gwo Dong Lin, Jordan M. Stoyanov
We study power-mixture type functional equations in terms of Laplace-Stieltjes transforms of probability distributions. These equations arise when studying distributional equations…
math.PR2020
Necessary and Sufficient Conditions for Unique Solution to Functional Equations of Poincare Type
Chin-Yuan Hu, Gwo Dong Lin
Distributional equation is an important tool in the characterization theory because many characteristic properties of distributions can be transferred to such equations. Using a no…