论文标题
在离散时间内适应弱拓扑的注释
A note on the adapted weak topology in discrete time
论文作者
论文摘要
适应性的弱拓扑是随机过程的弱拓扑扩展，旨在充分捕获基本过滤的特性。随着Bart-Beiglböck-p的最新工作。作为起点，本注释的目的是用拓扑参数恢复，这是由Backhoff-Bartl-Beiglböck-eder带来的引人入胜的结果，即在离散时间重合的所有适应性拓扑结构。我们还得出了这种拓扑的新特征，包括对马尔可夫过程和配备自然过滤的过程的痕迹的描述。为了强调论点的普遍性，我们还根据薄弱的Wasserstein度量的$ \ Mathbb r^d $措施的经典弱拓扑，该度量是基于Gozlan-Roberto-Samson-Tetali发起的弱最佳运输理论。
The adapted weak topology is an extension of the weak topology for stochastic processes designed to adequately capture properties of underlying filtrations. With the recent work of Bart--Beiglböck-P. as starting point, the purpose of this note is to recover with topological arguments the intriguing result by Backhoff-Bartl-Beiglböck-Eder that all adapted topologies in discrete time coincide. We also derive new characterizations of this topology including descriptions of its trace on the sets of Markov processes and processes equipped with their natural filtration. To emphasize the generality of the argument, we also describe the classical weak topology for measures on $\mathbb R^d$ by a weak Wasserstein metric based on the theory of weak optimal transport initiated by Gozlan-Roberto-Samson-Tetali.
