Duality Theorem for Stochastic Optimal Control Problem

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On the Relation Between Optimal Transport and Schrödinger Bridges: A Stochastic Control Viewpoint (2014, unknown): “We follow in the footsteps of Léonard [30,33], who investigated their relation, and of Mikami and Thieullen [31,44,45] who employed stochastic control and Schrödinger bridges to solve the optimal transport problem.”
A survey of the Schr\"odinger problem and some of its connections with optimal transport (2013, background): “Thieullen have proved a Kantorovich-type dual equality in [MT06] for (7.”
Applications of weak transport theory (2020, unknown): “where mass is transported along the trajectories of a semimartingale. As such, it also contains both martingale optimal transport [30, 13, 14], and the drift control framework of Mikami and Thieullen [41], as particular cases. We show that weak transport theory can be used to strengthen the main dua”
Causal transport plans and their Monge–Kantorovich problems (2013, background): “Thieullen (see [29], [28], [30], [31]) in close connexion to stochastic mechanics (see [24]).”
About the analogy between optimal transport and minimal entropy (2015, background): “Both [MT06] and [CGP] share the same stochastic optimal control viewpoint.”
Optimal transportation under controlled stochastic dynamics (2013, methodology): “1 of Mikami and Thieullen [30]; we report it here for completeness.”