| 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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| 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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