New approach to spectral theory of generalized second-order differential operators and its applications to probability theory
| Project/Area Number |
21540109
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | University of Tsukuba |
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Principal Investigator |
KASAHARA Yuji 筑波大学, 数理物質系, 教授 (60108975)
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| Co-Investigator(Kenkyū-buntansha) |
LIANG Song 筑波大学, 数理物質系, 准教授 (60324399)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 確率論 / Kreinの対応 / 1次元拡散過程 / 極限円 / 推移確率密度 / 推移確率 / スペクトル関数 / スペクトル関数の漸近挙動 |
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| Research Abstract |
It is well known that a linear diffusion is described by a generalized second-order differential operator. Therefore, the study of various quantities of linear diffusions is reduced to problems on the spectral functions. In the present study we obtained a necessary and sufficient condition on the asymptotic behavior of the spectral function. Furthermore, we also obtained some related results on the maximum process of the diffusion.
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Report
(4 results)
Research Products
(24 results)
