论文标题
改编的Wasestein SDE定律之间的距离
Adapted Wasserstein distance between the laws of SDEs
论文作者
论文摘要
我们考虑了标量时均匀随机微分方程定律之间的Bicausal最佳运输问题，并且我们确定了这些定律之间同步耦合的最佳性。该结果的证明是基于时间限制的，并揭示了同步耦合与著名的离散时间Knothe-Rosenblatt重排之间的新颖联系。我们还证明了拓扑相等的结果，仅限于连续时间过程的一定子集。我们通过示例来补充我们的主要结果，以显示最佳耦合如何在路径依赖性和多维设置中改变。
We consider the bicausal optimal transport problem between the laws of scalar time-homogeneous stochastic differential equations, and we establish the optimality of the synchronous coupling between these laws. The proof of this result is based on time-discretisation and reveals a novel connection between the synchronous coupling and the celebrated discrete-time Knothe--Rosenblatt rearrangement. We also prove a result on equality of topologies restricted to a certain subset of laws of continuous-time processes. We complement our main results with examples showing how the optimal coupling may change in path-dependent and multidimensional settings.
