论文标题
线性转移作为衡量措施的最低成本
Linear transfers as minimal costs of dilations of measures in balayage order
论文作者
论文摘要
在[5,6]中引入了概率分布之间的线性转移，以扩展最佳的质量运输理论，同时保留Kantorovich建立的重要二元性。这里显示的是，$ \ {0， +\ infty \} $ - 有价值的线性传输可以通过衡量适当函数锥的度量的特征来表征ch choquet的合适圆锥，而一般线性线性传输则扩展了balayage理论，通过要求“扫描”的“扫描”测量来优化某些成本函数。我们研究了坎多洛维奇运营商的双重类别，它们是马尔可夫运营商的自然且易于管理的扩展。它也是能力的重要子类，可以称为“凸功能性choquet能力”，因为它们扮演非线性地图与凸信封在任意数值函数中所做的相同作用。即将发表的论文[7]将研究其颈性特性及其应用。
Linear transfers between probability distributions were introduced in [5,6] in order to extend the theory of optimal mass transportation while preserving the important duality established by Kantorovich. It is shown here that $\{0, +\infty\}$-valued linear transfers can be characterized by balayage of measures with respect to suitable cones of functions à la Choquet, while general linear transfers extend balayage theory by requiring the "sweeping out" of measures to optimize certain cost functionals. We study the dual class of Kantorovich operators, which are natural and manageable extensions of Markov operators. It is also an important subclass of capacities, and could be called "convex functional Choquet capacities," since they play for non-linear maps the same role that convex envelopes do for arbitrary numerical functions. A forthcoming paper [7] will study their ergodic properties and their applications.
