2017 Fiscal Year Final Research Report
Systematic develpment of stochastic differential geometry associated with sub-Laplacians
| Project/Area Number |
15K04931
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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)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | サブラプラシアン / CR多様体 / サブリーマン多様体 / マリアバン解析 / 確率微分方程式 |
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| Outline of Final Research Achievements |
As for diffusion processes generated by degenerate second order differential operators and their images through smooth mappings, their realizations as Wiener functionals and applications to Diriclet problems and heat kernels are investigated. In particular, on CR manifolds and equiregular sub-Riemann manifolds, diffusion processes are constructed with the help of stochastic differential equations on frame bundles over them. In addition, such diffusion processes are used in the stochastic analytical approach to heat kernels.
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| Free Research Field |
確率解析
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