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arXiv · 2209.03243

Adapted Wasserstein distance between the laws of SDEs

Julio Backhoff-Veraguas·Sigrid Källblad·Benjamin A. Robinson
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Abstract

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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Julio Backhoff-Veraguas, Sigrid Källblad, Benjamin A. Robinson. 2022-09-07. Adapted Wasserstein distance between the laws of SDEs. https://doi.org/10.1016/j.spa.2025.104689

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