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Hokkaido University Preprint Series in Mathematics >
Optimal Transportation Problem by Stochastic Optimal Control
| Title: | Optimal Transportation Problem by Stochastic Optimal Control |
| Authors: | Mikami, Toshio Browse this author | | Thieullen, Michele Browse this author |
| Keywords: | optimal transportation | | Monge-Kantorovich problem | | Monge problem | | duality | | stochastic control | | Hamilton-Jacobi-Bellman pde | | value function | | vanishing viscosity | | semi-convex functions. |
| Issue Date: | 3-Feb-2005 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 690 |
| Start Page: | 1 |
| End Page: | 17 |
| Abstract: | We 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). |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69495 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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