A probabilistic view on the adapted Wasserstein distance

article A probabilistic view on the adapted Wasserstein distance epub_ahead yes Mathias Beiglböck author Susanne Pflügl author 8da18bd3-8437-11f1-a311-c814b8b76424 Stefan Schrott author JaMa department Causal optimal transport and adapted Wasserstein distance have applications in different fields from optimization to mathematical finance and machine learning. The goal of this article is to provide equivalent formulations of these concepts in classic probabilistic language. In particular, we prove a Skorokhod representation theorem for adapted weak convergence, reformulate the equivalence of stochastic processes using Markovian lifts, and give an expression for the adapted Wasserstein distance based on representing processes on a common stochastic basis. https://creativecommons.org/licenses/by/4.0/ Elsevier2026 eng Stochastic Processes and their Applications 0304-4149 2406.1981010.1016/j.spa.2026.105032 201 Beiglböck M, Pflügl S, Schrott S. A probabilistic view on the adapted Wasserstein distance. Stochastic Processes and their Applications. 2026;201. doi:<a href="https://doi.org/10.1016/j.spa.2026.105032">10.1016/j.spa.2026.105032</a> M. Beiglböck, S. Pflügl, and S. Schrott, “A probabilistic view on the adapted Wasserstein distance,” Stochastic Processes and their Applications, vol. 201. Elsevier, 2026. Beiglböck M, Pflügl S, Schrott S. 2026. A probabilistic view on the adapted Wasserstein distance. Stochastic Processes and their Applications. 201, 105032. Beiglböck, Mathias, Susanne Pflügl, and Stefan Schrott. “A Probabilistic View on the Adapted Wasserstein Distance.” Stochastic Processes and Their Applications. Elsevier, 2026. <a href="https://doi.org/10.1016/j.spa.2026.105032">https://doi.org/10.1016/j.spa.2026.105032</a>. Beiglböck, M., Pflügl, S., & Schrott, S. (2026). A probabilistic view on the adapted Wasserstein distance. Stochastic Processes and Their Applications. Elsevier. <a href="https://doi.org/10.1016/j.spa.2026.105032">https://doi.org/10.1016/j.spa.2026.105032</a> M. Beiglböck, S. Pflügl, S. Schrott, Stochastic Processes and Their Applications 201 (2026). Beiglböck, Mathias, et al. “A Probabilistic View on the Adapted Wasserstein Distance.” Stochastic Processes and Their Applications, vol. 201, 105032, Elsevier, 2026, doi:<a href="https://doi.org/10.1016/j.spa.2026.105032">10.1016/j.spa.2026.105032</a>. 223612026-07-19T22:01:45Z2026-07-20T12:46:53Z