Foundations of an anti-symmetric version of Malliavin calculus
| Project/Area Number |
23654056
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Ritsumeikan University |
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Principal Investigator |
AKAHORI Jiro 立命館大学, 理工学部, 教授 (50309100)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 反対称マリアバン解析 / クリフォード代数 / フェルミオン / ボゾン化 / タウ関数 / 確率面積 / 佐藤グラスマン多様体 / マリアバン解析 |
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| Research Abstract |
This project aimed to provide foundations to an anti-symmetric version of Malliavin calculus. As outputs, we obtained the following mathematical results. The first is that we have succeeded to obtain a probabilistic representation of tau functions of KP hierarchy, which fully extends the previous results on KdV one. The second is that we constructed a representation of Clifford algebra on Wiener space. Based on it, we also succeeded to construct a probabilistic Bosonization, which is the third of our main contributions in this project. Other than these, we have also obtained an interesting result on a relation between solitons of KdV equation and the term structure of interest rates in mathematical finance.
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Report
(4 results)
Research Products
(15 results)
