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A probabilistic view on the adapted Wasserstein distance

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  • Beiglböck, Mathias
  • Pflügl, Susanne
  • Schrott, Stefan

Abstract

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.

Suggested Citation

  • Beiglböck, Mathias & Pflügl, Susanne & Schrott, Stefan, 2026. "A probabilistic view on the adapted Wasserstein distance," Stochastic Processes and their Applications, Elsevier, vol. 201(C).
    • Handle: RePEc:eee:spapps:v:201:y:2026:i:c:s030441492600164x
    DOI: 10.1016/j.spa.2026.105032
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