Stochastic analysis on infinite dimensional spaces and its related differential operators
| Project/Area Number |
26400134
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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 | Okayama University |
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Principal Investigator |
KAWABI HIROSHI 岡山大学, 自然科学研究科, 教授 (80432904)
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| Co-Investigator(Renkei-kenkyūsha) |
HIROKAWA MASAO 広島大学, 大学院工学研究院, 教授 (70282788)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 確率解析 / 微分作用素 / 中心極限定理 / 確率偏微分方程式 / rough path理論 / 結晶格子 / ベキ零被覆グラフ / ランダムウォーク / 確率論 / 一意性定理 / 離散幾何解析 / ラフパス理論 / マリアヴァン解析 |
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| Outline of Final Research Achievements |
I mainly studied uniqueness problems of differential operators and the corresponding stochastic dynamics on infinite dimensional spaces via stochastic analysis. In particular, I considered Dirichlet forms given by space-time quantum fields with interactions of exponential type, called exp(\phi)_{2}-measure, in Euclidean QFT, and proved strong uniqueness of Dirichlet operators of the corresponding Dirichlet operator. I also discussed the related singular stochastic partial differential equation. Besides, I studied central limit theorems for non-symmetric random walks on both crystal lattices and nilpotent covering graphs from a viewpoint of discrete geometric analysis, and discussed its application to rough path theory. Finally, I proved that the space of Gaussian measures on an abstract Wiener space becomes a Hilbert-Riemannian manifold with non-positive sectional curvatures.
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Report
(4 results)
Research Products
(36 results)
