2017 Fiscal Year Final Research Report
Superposition of diffusion processes on a high-dimensional Tube
Project/Area Number |
26800060
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Basic analysis
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Research Institution | Nara Women's University |
Principal Investigator |
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Project Period (FY) |
2014-04-01 – 2018-03-31
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Keywords | 収束定理 / 拡散過程 / 斜積拡散過程 / ディリクレ形式 / ブラウン運動 / 高次元チューブ |
Outline of Final Research Achievements |
We considered Limit theorems for diffusion processes on a high-dimensional tube. The sequence of diffusion processes are given by direct product diffusion processes D and Y and the time changed diffusion processes where D is a one-dimensional diffusion process and Y is a skew product diffusion of a one-dimensional diffusion process R and d-1 dimensional spherical Brownian motion by means of positive continuous additive functional of R. We show a limit theorem for a sequence of time changed process under some assumptions for underlying measures and we also obtained concrete expressions of the Dirichlet forms corresponding to time changed processes, which may be of non-local type on a tube caused by degeneracy of the underlying measures.
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Free Research Field |
数物系科学
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