Abstract

We consider the transformations of independent random variables over a linearly ordered finite set (a chain) by the join and meet operations. We investigate the possibility of approximating an arbitrary probability distribution on a chain by means of a (possibly iterated) application of the join and meet operations to independent random variables with distributions from a given set. We establish some conditions under which the approximation is impossible and the conditions when it becomes possible.

中文翻译：

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关于有限链上随机变量的逼近

摘要

我们考虑通过join和meet操作在线性有序有限集（链）上对独立随机变量的变换。我们研究了通过联接的（可能迭代的）应用逼近链上任意概率分布的可能性，并满足对具有给定集合分布的独立随机变量的操作。我们建立了一些条件，在这些条件下不可能近似，而在可能的条件下近似。