Stochastic Analysis on nonlinear sets
| Project/Area Number |
19740047
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Shinshu University |
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Principal Investigator |
OTOBE Yoshiki Shinshu University, 理学部, 講師 (30334882)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥3,710,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥510,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,500,000 (Direct Cost: ¥1,500,000)
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| Keywords | マリアバン解析 / 確率偏微分方程式 / 発散定理 / 部分積分 / マリアヴァン解析 / パーコレーション / フラクタル格子 / 確率論 / 渡辺合成 |
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| Research Abstract |
We have formulated a divergence formula on convex sets in the Gaussian space which include usual Wiener spaces. We found that a certain regularity of the maximal of the processes under the Gaussian measure plays an essential role rather than Markov properties which was believed. We also succeeded in recovering known formulae using Markov properties then, which is a concrete expression of our divergence formulae. We have also obtained a critical probability for a percolation on a fractal set. We have succeeded in visualizing a motion of interacting particles, solutions to stochastic partial differential equations driven by Levy type noises.
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Report
(4 results)
Research Products
(25 results)
