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Dynamic characterization of barycentric optimal transport problems and their martingale relaxation
Ivan Guo, Severin Nilsson, Johannes Wiesel · 2025-11-26 · via math.PR updates on arXiv.org

We extend the Benamou-Brenier formula from classical optimal transport to weak optimal transport and show that the barycentric optimal transport problem studied by Gozlan and Juillet has a dynamic analogue. We also investigate a martingale relaxation of this problem, and relate it to the martingale Benamou-Brenier formula of Backhoff-Veraguas, Beiglböck, Huesmann and Källblad.

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