2013 Fiscal Year Final Research Report
Stochastic analysis and its application to differential operators
| Project/Area Number |
23540183
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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 | Aoyama Gakuin University (2012-2013)
Yamagata University (2011) |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
TANIGUCHI Setsuo 九州大学, 基幹教育院, 教授 (70155208)
JIMBO Masakazu 名古屋大学, 大学院・情報科学研究科, 教授 (50103049)
WAKI Katsushi 山形大学, 理学部, 教授 (30250591)
HIRAO Masatake 東京女子大学, 現代教養学部, 講師 (90624073)
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| Project Period (FY) |
2011 – 2013
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| Keywords | ベッセル過程 / 到達時刻 / 変形ベッセル関数 |
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| Research Abstract |
The most important result is the result on the first hitting times of Bessel processes which is one of the fundamental stochastic processes. When the starting point is far from the arigin than the terminal point, we have shown fairly simple expressions for the probability densities by means of the zeros of the modified Bessel functions. As applications, we have investigated the asymptotic behavior of the probability densities and the tail probabilities. We have also shown the asymptotics of the expected volume of the tubar neighborhood of Brownian motions. On the other hand, we have found some algebraic equations which are satisfied by the zeros of the Modified Bessel functions.
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