论文标题
双子型蒙格映射的密度
Denseness of biadapted Monge mappings
论文作者
论文摘要
改编或因果运输理论旨在将经典的最佳运输从概率措施扩展到随机过程。从技术层面上讲，新颖性是限制到bicausal的耦合，即满足反映随机过程中信息时间演变的特性。我们表明，在绝对连续的边缘的情况下，确切地将Bicausal耦合的集合作为（Bi-）适应过程的闭合而获得。也就是说，我们获得了坎托洛维奇运输计划中蒙加耦合密度的经典结果的类似物：bicausal运输计划代表了与坎多洛维奇运输计划相同的方式放松改编映射的方式，这是对猴子映射的适当放松。
Adapted or causal transport theory aims to extend classical optimal transport from probability measures to stochastic processes. On a technical level, the novelty is to restrict to couplings which are bicausal, i.e. satisfy a property which reflects the temporal evolution of information in stochastic processes. We show that in the case of absolutely continuous marginals, the set of bicausal couplings is obtained precisely as the closure of the set of (bi-) adapted processes. That is, we obtain an analogue of the classical result on denseness of Monge couplings in the set of Kantorovich transport plans: bicausal transport plans represent the relaxation of adapted mappings in the same manner as Kantorovich transport plans are the appropriate relaxation of Monge-maps.
