| Project/Area Number |
18K03343
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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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| Review Section |
Basic Section 12010:Basic analysis-related
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| Research Institution | Aoyama Gakuin University |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 確率的変分問題 / 粘性ハミルトン・ヤコビ方程式 / 確率最適制御 / マルコフ決定過程 / 割引因子 / ベルマン方程式 / エルゴード問題 / 一般化主固有値 |
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| Outline of Final Research Achievements |
We obtained some mathematical results on the problem of stochastic calculus of variations, which is a stochastic version of the classical problem of calculus of variations originating from geometric optics and brachystochrone. We investigated how the long time behavior of the optimal trajectory changes with a perturbation of the potential term and gave, in terms of the parameters in the model, an explicit condition for a phase transition. We also constructed a discrete model corresponding to the above continuous problem and showed that similar phenomena can be observed in that model.
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| Academic Significance and Societal Importance of the Research Achievements |
連続型確率的変分問題の臨界性理論に関する既知の結果を大幅に改善することができた。特に、粘性ハミルトン・ヤコビ方程式の解の性質や確率的変分問題の最適軌道に関する精密な評価式を得ることができた。また、これまではあまり考察されてこなかった確率的変分問題の離散版に相当するモデルを構築することができた。これらの結果より、確率的変分問題の臨界性理論に関する研究のさらなる学術的な進展が期待される。
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