A new development of stochastic differential geometry associated with degenerate differential operators
| Project/Area Number |
24540178
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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 |
Basic analysis
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| Research Institution | Kyushu University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
MATSUMOTO Hiroyuki 青山学院大学, 理工学部, 教授 (00190538)
SHIRAI Tomoyuki 九州大学, マス・フォア・インダストリ研究所, 教授 (70302932)
UEMURA Hideaki 愛知教育大学, 教育学部, 教授 (30203483)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | CR-多様体 / CR-ブラウン運動 / 熱核 / 確率微分幾何 / Malliavin解析 |
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| Outline of Final Research Achievements |
A diffusion process generated by a sub-Laplacian, which is a real part of the Kohn-Rossi Laplacian on a CR-manifold, is constructed in a globally geometrical manner by extending the Elles-Elworthy-Malliavin approach to the Brownian motion on a Riemannian manifold. Using the diffusion process (CR-Brownian motion), the heat equation and the Dirichlet problem associated with the sub-Laplacian are investigated in a stochastically analytic manner.
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Report
(4 results)
Research Products
(4 results)
