改编了Wasserstein距离SDEs定律

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications Pub Date : 2025-05-27 DOI:10.1016/j.spa.2025.104689

Julio Backhoff-Veraguas , Sigrid Källblad , Benjamin A. Robinson

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引用次数: 0

摘要

考虑标量时间齐次随机微分方程律间的双因果最优输运问题，建立了这些律间同步耦合的最优性。这一结果的证明是基于时间离散化的，并揭示了同步耦合与著名的离散时间Knothe-Rosenblatt重排之间的新联系。我们还证明了拓扑结构在连续时间过程定律的某一子集上的等价性。我们用一些例子来补充我们的主要结果，这些例子展示了最优耦合在路径依赖和多维设置中如何变化。

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Adapted Wasserstein distance between the laws of SDEs

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.

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来源期刊

Stochastic Processes and their Applications 数学-统计学与概率论

CiteScore

2.90

自引率

7.10%

发文量

180

审稿时长

23.6 weeks

期刊介绍： Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests. Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.