Titlebook: Stochastic Optimal Transportation; Stochastic Control w Toshio Mikami Book 2021 The Author(s), under exclusive license to Springer Nature S

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Stochastic Optimal Transportation Problem,re fixed. In particular, we give the Duality Theorems for the SOTs and a sufficient condition for the finiteness of the minimum in the SOT with given initial and terminal distributions. We also show that the zero-noise limit of Schrödinger’s problem exists and the limit solves Monge’s problem with a

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Stochastic Optimal Transportation Problem,initial and terminal distributions. We also show that the zero-noise limit of Schrödinger’s problem exists and the limit solves Monge’s problem with a quadratic cost and that the zero-noise limit of the Duality Theorem for the SOT gives the Duality Theorem for the OT.

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Introduction,t is also a generalization of Schrödinger’s problem and is related to Nelson’s stochastic mechanics. We briefly describe the OT and Schrödinger’s problems in such a way that one can compare the similarities between them.

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