The quadratic barycentric transport cost equals the infimum of an expected kinetic-energy integral over semimartingales, and the optimal processes are geodesics with Markovian dynamics.
Martingale benamou–brenier
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On the quadratic barycentric transport problem
The quadratic barycentric transport cost equals the infimum of an expected kinetic-energy integral over semimartingales, and the optimal processes are geodesics with Markovian dynamics.