A study of generalization of stochastic optimal transportation problems and mean field games
| Project/Area Number |
26400136
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Tsuda University |
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Principal Investigator |
Mikami Toshio 津田塾大学, 学芸学部, 教授 (70229657)
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| Project Period (FY) |
2014-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 確率最適輸送問題 / Schrodinger汎関数方程式 / 平均場偏微分方程式 / モーメント確率測度 / Master方程式 / Witzenhausen問題 / Schrodingerの汎関数方程式 / 調和過程 / Gateaux 微分 / 直積測度 |
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| Outline of Final Research Achievements |
We gave a sufficient condition under which stochastic optimal transportation problem is finite.
Suppose that S is a sigma compact metric space and the space of all probability measures on S is endowed with the strong topology. Then we proved the continuity and Borel measurability of the solution to Schrodinger’s functional equation with respect to marginal distributions and a kernel function, provided S is compact and noncompact respectively. Suppose, in addition, that S is complete and separable and that S is endowed with the weak topology instead. Then we proved the continuity of the solution. As an application, we constructed a convex function of which the moment probability measure is a give probability measure.
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| Academic Significance and Societal Importance of the Research Achievements |
確率最適輸送問題が有限であるための十分条件を与えたことにより、確率最適輸送理論の基礎が完成した。
調和経路過程を平均場ゲーム理論の枠組みで研究できることを示した。特に、それにより、確率最適輸送問題とその一般化を平均場ゲーム理論の枠組みで発展させることができる可能性を示せた。また、Schrodinger汎関数方程式の滑らかさの研究とその応用を示すことにより、確率最適輸送問題を確率測度空間上の汎関数方程式の問題として発展しうる可能性も出てきた。
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Report
(6 results)
Research Products
(23 results)
