论文标题
通过功能混合类型的功能方程来表征概率分布
Characterization of Probability Distributions via Functional Equations of Power-Mixture Type
论文作者
论文摘要
我们根据概率分布的laplace-stieltjes变换来研究功率混合型功能方程。当研究Z = X + TZ类型的分布方程时，会出现这些方程，其中t是已知的随机变量，而变量z是通过x定义的，我们希望“找到”X。我们为此类功能方程提供了必要的条件，以使其具有独特的解决方案。唯一性等同于概率分布的表征属性。我们提出的结果是新的或扩展并改善有关复合指数和复合辉石类型功能方程的先前结果。特别是，我们对J. Pitman和M. Yor在2003年提出的一个问题给出了另一个肯定的答案。我们提供了明确的说明性示例并处理相关主题。
We study power-mixture type functional equations in terms of Laplace-Stieltjes transforms of probability distributions. These equations arise when studying distributional equations of the type Z = X + TZ, where T is a known random variable, while the variable Z is defined via X, and we want to `find' X. We provide necessary and sufficient conditions for such functional equations to have unique solutions. The uniqueness is equivalent to a characterization property of a probability distribution. We present results which are either new or extend and improve previous results about functional equations of compound-exponential and compound-Poisson types. In particular, we give another affirmative answer to a question posed by J. Pitman and M. Yor in 2003. We provide explicit illustrative examples and deal with related topics.
