Applications of stochastic calculus to the KdV equation and hierarchy
| Project/Area Number |
18340038
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kyushu University |
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Principal Investigator |
TANIGUCHI Setsuo Kyushu University, 大学院・数理学研究院, 教授 (70155208)
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| Co-Investigator(Kenkyū-buntansha) |
FUKAI Yasunari 九州大学, 大学院・数理学研究院, 助手 (00311837)
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥7,450,000 (Direct Cost: ¥6,100,000、Indirect Cost: ¥1,350,000)
Fiscal Year 2009: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2008: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2007: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2006: ¥1,600,000 (Direct Cost: ¥1,600,000)
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| Keywords | 確率解析 / 確率振動積分 / KdV方程式 / KdV階層 / 2次ウィナー汎関数 / オレンシュタイン・ウーレンベッマ過程 / 非可換調和振動子 / 確率面積 / 1-ソリトン / 二次ウィナー汎関数 / 広田微分 / 2次ウイナー汎関数 |
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| Research Abstract |
A deep study of the theory of Stochastic Calculus was made, aiming to apply stochastic oscillatory integrals to the KdV equation and the KdV hierarchy. Several new results in Stochastic Calculus are obtained : an application of stochastic representation to the convergence of reflectionless potentials, concrete expression of stochastic oscillatory integral, a Wiener integral representation approach to non commutative harmonic oscillator. Moreover, a new Wiener functional of the Brownian sheet was investigated. Finally, the relationship between stochastic oscillatory integrals and Jacobi equations was studied to understand stochastic oscillatory integrals from the point of view of algebraic analysis.
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Report
(6 results)
Research Products
(40 results)
