2023-03-22T19:57:39Zhttps://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, Micheleoptimal 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 UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69495info:doi/10.14943/83841https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69495/1/pre690.pdfHokkaido University Preprint Series in Mathematics6901172005-02-03engpublisher