Adapted Wasserstein distance between the laws of SDEs
Probability
2025-10-10 v5
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
Cite
@article{arxiv.2209.03243,
title = {Adapted Wasserstein distance between the laws of SDEs},
author = {Julio Backhoff-Veraguas and Sigrid Källblad and Benjamin A. Robinson},
journal= {arXiv preprint arXiv:2209.03243},
year = {2025}
}