Adapted Wasserstein distance between the laws of SDEs

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

Stochastic Processes and their Applications, 2025, vol. 189, issue C

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.

Keywords: Knothe–Rosenblatt rearrangement; Adapted Wasserstein distance; Bicausal optimal transport; Stochastic differential equations; Optimal couplings (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104689

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