| Project/Area Number |
10640147
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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 | Osaka University (1999)
Tohoku University (1998) |
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Principal Investigator |
AIDA Shigeki Graduate School of Engineering Science, Osaka University, Associate Professor, 大学院・基礎工学研究科, 助教授 (90222455)
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| Co-Investigator(Kenkyū-buntansha) |
KUWAE Kazuhiro 横浜市立大学, 理学部, 助教授 (80243814)
SEKIME Jun 大阪大学, 大学院・基礎工学研究科, 講師 (50314399)
NAGAI Hideo 大阪大学, 大学院・基礎工学研究科, 教授 (70110848)
TOSHIDA Noluo 京都大学, 大学院・理学研究科, 講師 (40240303)
KAZUM Tetsuya 大阪府立大学, 総合科学部, 講師 (40224422)
古畑 仁 東北大学, 大学院情報科学研究科, 助手 (80282036)
岡田 正巳 東北大学, 大学院情報科学研究科, 教授 (00152314)
浦川 肇 東北大学, 大学院情報科学研究科, 教授 (50022679)
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| Project Period (FY) |
1998 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 1999: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 1998: ¥1,800,000 (Direct Cost: ¥1,800,000)
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| Keywords | Logarithmic Soboles inequality / Spectral Gap / Loop Space / 対数リボレフ不等式 / ディソクレ形式 / ギッブス測度 / ハルナック不等式 |
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| Research Abstract |
The results obtained for 1998-1999 are as follows :
1. We proved a Varadhan type asymptotics of diffusion processes in Wiener spaces
2. We gave an irreducibility criterion of diffusion processes on a subset in an Wiener space in terms of a certain connectivity of the subset.
3. We proved a Clark-Ocone formula for pinned Brownian motion.
The following are explanations of the aboves.
1. : This is a generalization of the Fang's results for Ornstein-Uhlenbeck processes to more general diffusion coefficients.
2. : The head investigator proved an irreducibility theorem for diffusion processes on loop spaces using Kusuoka's theorem. In this work, the head investigator proved the generalization.
3. : As an application, the head investigator proved a logarithmic Sobolev inequality on loop space over hyperbolic spaces.
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