The study of asymptotic behavior of Wiener sausages for stochastic processes
| Project/Area Number |
24540181
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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 | Kumamoto University |
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Principal Investigator |
Hamana Yuji 熊本大学, 自然科学研究科, 教授 (00243923)
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| Research Collaborator |
MATSUMOTO Hiroyuki
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 確率論 / 確率解析 / ベッセル過程 / 到達時刻 / Wiener sausage / 変形ベッセル関数 / Bessel 過程 / Bessel 関数 / ブラウン運動 / Gegenbauer 多項式 / 歪積表現 / Ornstein-Uhlenbeck 過程 / ベッセル関数 |
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| Outline of Final Research Achievements |
We give the joint distribution of the hitting time and site of a Brownian motion with and without constant drift. This result yields the formula for the expected volume of the Wiener sausages of Brownian motions and their asymptotic behavior for large time. Moreover we obtain the asymptotics of tail probabilities of first hitting times of Bessel processes with and without the drift. In addition, we find that zeros of Bessel function of the second kind are holomorhic with respect to the indices and establish the method of their calculation with a general-purpose computer soft of computations, Mathematica for example.
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Report
(5 results)
Research Products
(17 results)
