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Adapted Wasserstein distance between the laws of SDEs

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

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.

Suggested Citation

  • Backhoff-Veraguas, Julio & Källblad, Sigrid & Robinson, Benjamin A., 2025. "Adapted Wasserstein distance between the laws of SDEs," Stochastic Processes and their Applications, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:spapps:v:189:y:2025:i:c:s0304414925001309
    DOI: 10.1016/j.spa.2025.104689
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