Infinite-Dimensional Stochastic approach to Geometrical Objects

几何对象的无限维随机方法

• 批准号: 17540124
• 负责人: MITOMA Itaru
• 金额: $ 2.05万
• 依托单位: Saga University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-17540124/
• 关键词: Chern-Simons integral; Wiener space; Wilson line; Holonomy; Topological invariant; Topological field theory; Superstring; Wiener空間; リンク不変量; 漸近展開; チャーン・サイモンズ理論; ウィルソンループ; リンク数; ファインマン積分

We,(Mitoma-Nishikawa),gave a mathematical definition for perturbative 1-loop approximation of the Chern-Simons integral with respect to the Wilson lines in an abstract Wiener space setting and proved the asymptotic expansion theorem. Further we calculate the copefficients for 3-dimensional surface and obtained link invariants. The result is now prepared for submission. We,(Albeverio-Mitoma),gave mathematical definitions for finite part and asymptotic estimate for infinite part of perturbative Chern-Simons integral via Wiener space. The result is appeared in SFB,611 in Bonn University.

我们（Mitoma-Nishikawa）给出了抽象Wiener空间中关于Wilson线的chen - simons积分的微扰1环近似的数学定义，并证明了渐近展开定理。进一步计算了三维曲面的系数，得到了连杆不变量。结果现在准备提交。我们（Albeverio-Mitoma）通过Wiener空间给出了摄动chen - simons积分有限部分的数学定义和无限部分的渐近估计。结果发表在波恩大学的SFB，611上。

项目成果

On the Quadratic Wiener Functional Associated with the Malliavin Derivative of the Square Norm of Brownian Sample Path on Interval

区间上布朗样本路径平方范数的Malliavin导数的二次维纳泛函

• 发表时间: 2006
• 期刊: Electron. Comm. Probab. 116-2
• 作者: Taniguchi;Setsuo
• 通讯作者: Setsuo

A note on random upper semicontinuous functions

关于随机上半连续函数的注解

• 发表时间: 2006
• 期刊: Soft Method for Integrated Uncertainty Modelling
• 作者: Hung T.Nguen;Yukio Ogura;Santi Tasena;Hien Tran
• 通讯作者: Hien Tran

On some metrics compatible with the Fell-Matheron topology

• DOI: 10.1016/j.ijar.2006.12.008
• 发表时间: 2007-09
• 期刊: Int. J. Approx. Reason.
• 作者: Y. Ogura

Sampling formulae for symmetric selection

• DOI: 10.1214/ecp.v10-1159
• 发表时间: 2005-11-14
• 期刊: ELECTRONIC COMMUNICATIONS IN PROBABILITY
• 影响因子: 0.5
• 作者: Handa, K

Strong law of large numbers for independent fuzzy set-valued random variables

独立模糊集值随机变量的强大数定律

• 发表时间: 2006
• 期刊: Fuzzy Sets and Systems 157
• 作者: Shoumei Li;Yukio Ogura
• 通讯作者: Yukio Ogura