Research on explicit numerical methods for high-dimensional stochastic differential equations
| Project/Area Number |
17K05369
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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 |
Foundations of mathematics/Applied mathematics
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| Research Institution | Kyushu Institute of Technology |
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Principal Investigator |
Komori Yoshio 九州工業大学, 大学院情報工学研究院, 准教授 (20285430)
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| Project Period (FY) |
2017-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 陽的解法 / 確率微分方程式 / ルンゲ・クッタ・チェビシェフ / 確率遅延微分方程式 / Exponential Runge-Kutta / 弱い意味で二次の近似 / 硬い方程式 / Magnus-type method / 半線形確率微分方程式 / 数値的安定性 / 陽的数値解法 / exponential method |
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| Outline of Final Research Achievements |
In order to understand phenomena in many fields such as Biochemistry, Physics and Finance, we can utilize mathematical models and they are helpful for us to predict how a phenomenon evolves as time goes. The mathematical models are usually described by differential equations such as ordinary differential equations (ODEs). In the present research project, we have derived new numerical methods for stochastic differential equations (SDEs), which are ODEs with noise terms. They will help us to investigate the time evolutions of phenomena described by SDEs.
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| Academic Significance and Societal Importance of the Research Achievements |
確率偏微分方程式を空間方向に離散化すると高い次元のSDE が現れる. 一般的に,これは数値的に解きにくいstiff な問題になる. 本研究課題に挙げた数値解法は, それを高精度で高速に解くことができる.
数理解析に対する要求の高まりとともに, 確率的な振る舞いを考慮した数理モデルが今後様々な分野に広がることが予想される. したがって，本研究課題の成果は将来的に非常に広範な分野に影響を及ぼすと考えられる.
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Report
(7 results)
Research Products
(24 results)
