Development of stochastic analysis on spaces with anomalous structures
| Project/Area Number |
21740094
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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 |
Basic analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
HINO Masanori 京都大学, 大学院・情報学研究科, 准教授 (40303888)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 確率解析 / Dirichlet形式 / フラクタル / 無限次元空間 / 対称拡散過程 / 拡散過程 / Riemann構造 / 各点指数 / 内在的距離 / 測地距離 / Wiener空間 / Sobolev空間 / 微分構造 / マルチンゲール次元 / 自己相似集合 / ラフパス理論 / 新古典不等式 |
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| Research Abstract |
In this research project, we developed theories related to stochastic analysis that were suitable for the study of spaces with anomalous structures, taking applications into consideration. In particular, we obtained some new results on the concepts of dimensions, metrics, and local structures of spaces derived by diffusion processes on fractals. Moreover, we solved the conjecture on the neo-classical inequality, and proved several properties on function spaces on infinite-dimensional state spaces.
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Report
(4 results)
Research Products
(27 results)
