Conditions for the existence of a joint distribution for the given marginal distributions (Q1878725)

This paper finds necessary and sufficient conditions for solvability of the following inverse problem: Given three two-dimensional probability distributions \({\mathbf P_{xy}}\), \({\mathbf P_{yz}}\), and \({\mathbf P_{zx}}\), find a three-dimensional distribution \({\mathbf P}\) such that these distributions are marginal for it, i.e., are exactly its first, second, and third components, respectively.