1999 Fiscal Year Final Research Report Summary
Siochastic Analysis on loop spaces
| 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)
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| Project Period (FY) |
1998 – 1999
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| Keywords | Logarithmic Soboles inequality / Spectral Gap / Loop Space |
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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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