| Project/Area Number |
22KF0158
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| Project/Area Number (Other) |
21F50732 (2021-2022)
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| Research Category |
Grant-in-Aid for JSPS Fellows
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| Allocation Type | Multi-year Fund (2023)
Single-year Grants (2021-2022) |
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| Section | 外国 |
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| Review Section |
Basic Section 12010:Basic analysis-related
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| Research Institution | Shinshu University |
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Principal Investigator |
謝 賓 信州大学, 学術研究院理学系, 教授 (50510038)
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| Co-Investigator(Kenkyū-buntansha) |
ZHU MIN 信州大学, 学術研究院理学系, 外国人特別研究員
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| Project Period (FY) |
2023-03-08 – 2024-03-31
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| Project Status |
Completed (Fiscal Year 2023)
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| Budget Amount *help |
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 2023: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2022: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2021: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | anisotropic / compactness / Galerkin approximation / Singular coefficient / p-Laplacian / delay / BDG inequality / distribution dependent / transformation / approximation / SPDEs / alpha-stable / Euler-Maruyama |
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| Outline of Research at the Start |
継続課題のため、記入しない。
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| Outline of Annual Research Achievements |
The achievements are about the studies on anisotropic stochastic partial differential equations (SPDEs) and numerical schemes for stochastic differential equations (SDEs).
Under weak assumptions, especially locally monotonic one, the existence and uniqueness of probabilistically strong solutions to anisotropic SPDEs is obtained by the variational approach. The Galerkin approximation and compactness argument are developed. Such result is expressed by two special and important anisotropic SPDEs, one is the anisotropic stochastic reaction-diffusion and the other is anisotropic stochastic Navier-Stokes equation.
The convergence of numerical schemes for stochastic differential equations with singular drift and alpha-stable noise is studied. By choosing a suitable approximation method to simulate the segment process, the convergence rate of the Euler-Maruyama scheme associated with the weakly interacting system for path-distribution dependent SDEs is obtained. To overcome the difficulties from the singular drift and the multiplicative noise, we establish a deterministic inequality and refine the regularity of solutions to the associated Kolmogorov equation, and thus obtain strong convergence of Euler-Maruyama scheme associated stochastic systems considered.
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