Stochastic analysis and the Hormander type operators on infinite dimensional spaces
| Project/Area Number |
20740076
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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 | Okayama University |
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Principal Investigator |
KAWABI Hiroshi Okayama University, 大学院・自然科学研究科, 准教授 (80432904)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 確率解析 / マリアヴァン解析 / Rough Path理論 / 微分作用素 / 一意性問題 / Riesz変換 / 経路空間 / Gibbs測度 / 一意性定理 / rough path理論 |
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| Research Abstract |
I studied some properties on the the Hormander type operators on infinite dimensional spaces by applying Malliavin calculus, rough path analysis, SPDEs, and Dirichlet form. In particular, I proved strong uniqueness of Dirichlet operators for Gibbs measures on an infinite volume path space, and constructed a unique strong solution for the corresponding SPDE via the Dirichlet form approach. Besides, I studied precise asymptotic behavior of some functional integrations for a class of infinite dimensional stochastic processes which include the Brownian motion on loop spaces.
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Report
(4 results)
Research Products
(45 results)
