2016 Fiscal Year Final Research Report
Toward a foundation of leafwise stochastic calculus on foliated spaces
| Project/Area Number |
26610024
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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 | Osaka University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
SUGITA Hiroshi 大阪大学, 大学院理学研究科, 教授 (50192125)
HIBI Masanori 京都大学, 大学院理学研究科, 教授 (40303888)
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| Research Collaborator |
SUZAKI Kiyotaka
TOKUNAGA Yusuke
IKEDA Takuya
SUZUKI Shintaro
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | 確率解析 / ブラウン運動 / 葉層付き空間 / 各葉拡散過程 / 中心極限定理 |
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| Outline of Final Research Achievements |
A foliated space is a family of manifolds each of which is called a leaf satisfying some geometric conditions. A leafwise Brownian motion on a foliated space is a diffusion process obtained by combining Brownian motions on leaves provided that each leaf is insulated from the others. We tried to establish a foundation of stochastic analysis on foliated space via the leafwise Brownian motion. There are many processes in order to finish it. We verified that most processes are finished. But a few of them are still in construction because of technical difficulties. As by-products we obtain a several results including a central limit theorem for leafwise Brownian motions on mapping tori.
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| Free Research Field |
確率論
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