2023-12-09T11:43:32Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/694952022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Optimal Transportation Problem by Stochastic Optimal ControlMikami, ToshioThieullen, Micheleopen accessoptimal transportationMonge-Kantorovich problemMonge problemdualitystochastic controlHamilton-Jacobi-Bellman pdevalue functionvanishing viscositysemi-convex functions.410We solve optimal transportation problem using stochastic optimal control theory. Indeed, for a super linear cost at most quadratic at infinity, we prove Kantorovich duality theorem by a zero noise limit (or vanishing viscosity) argument.. We also obtain a characterization of the support of an optimal measure in Monge-Kantorovich minimization problem (MKP) as a graph. Our key tool is a duality result for a stochastic control problem which naturally extends (MKP).Department of Mathematics, Hokkaido University2005-02-03engdepartmental bulletin paperVoRhttps://doi.org/10.14943/83841http://hdl.handle.net/2115/6949510.14943/83841Hokkaido University Preprint Series in Mathematics690117https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69495/1/pre690.pdfapplication/pdf144.71 KB2005-02-03