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Absolutely Continuous Curves of Stochastic Processes
Beatrice Acciaio, Daniel Kr\v{s}ek, Gudmund Pammer, Marco Rodrigues
https://arxiv.org/abs/2506.13634 h…

Absolutely Continuous Curves of Stochastic Processes
We study absolutely continuous curves in the adapted Wasserstein space of filtered processes. We provide a probabilistic representation of such curves as flows of adapted processes on a common filtered probability space, extending classical results to the adapted setting. Moreover, we characterize geodesics in this space and derive an adapted Benamou--Brenier-type formula by reformulating adapted optimal transport as an energy minimization problem. As an application, we obtain a Skorokhod-type …