The expansion of the criticality theory for stochastic optimal control and its applications
| Project/Area Number |
15K04935
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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 | Aoyama Gakuin University |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
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)
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| Keywords | 確率最適制御 / 粘性Hamilton-Jacobi方程式 / エルゴード問題 |
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| Outline of Final Research Achievements |
In this research, we studied the criticality theory for a class of nonlinear partial differential equations, called viscous Hamilton-Jacobi equations, by using both probabilistic and PDE theoretic methods. More specifically, we clarified the relationship between “phase transition” phenomena arising in stochastic optimal control and the generalized principal eigenvalue for viscous Hamilton-Jacobi equations. We especially quantified such phase transitions in terms of the space dimensions as well as the intensity of nonlinearity of the equation.
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Report
(4 results)
Research Products
(14 results)
