| Project/Area Number |
18540170
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Aichi University of Education |
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Principal Investigator |
UEMURA Hideaki Aichi University of Education, Fuculty of Education, 教授 (30203483)
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| Project Period (FY) |
2006 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥1,250,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥150,000)
Fiscal Year 2007: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2006: ¥600,000 (Direct Cost: ¥600,000)
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| Keywords | Stochastic Analvsis / Positive Continuous Additive Function / Brownian Motion / Local Time / Revuz measure / Riesz kernel / 極限定理 / 多次元ブラウン運動 / マリアヴァン解析 |
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| Research Abstract |
We studied positive continuous additive functionals (PCAF in abbr.) of multidimensional Brownian motions in the framework of generalized Wiener functionals.
1. We defined a PCAF of multidimensional Brownian motions in the framework of generalized Wiener functionals. We clarified the structure of PCAF through the corresponding characteristic and Revuz measure, which are well-defined also in our cases.
(1) We defined a PCAF of multidimensional Brownian motions in the framework of generalized Wiener functionals, mod obtained the representation by the Brownian local line and the Revuz measure associated to PCAE
(2) We obtained that the Revue measure associated to the PCAF constructed by a Radon measure is identical with the original Radon measure, and that the PCAF constructed by the Revuz measure of a PCAF is identical with the original PCAF.
(3) We obtained the integrability condition on a Radon measure to identify the Sobolev space to which the PCAF constructed by a Radon measure belongs. As a result we showed that the PCAF constricted by the uniform measure on two or three dimensional Sierpinski gasket is square itegrable.
2. We studied the PCAF corresponding to the Riesz kernel.
(1) We constructed the PCAF corresponding to the Riesz kernel (Riesz PCAF in abbr) and obtained the occupation time formula. We also obtained the continuity of the Riesz PCAF with respect to space parameter in the sense of mean convergence of order 1.
(2) We obtained the limit theorem in which the Riesz PCAF appears, which has been done by T.Yamada in one dimensional Brownian motion case.
(3) We obtained the relation between the Biesz, PCAF and the Brewnian heal time
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