New development of infinite dimensional stochastic analysis and its applications

无限维随机分析新进展及其应用

• 批准号: 21244009
• 负责人: AIDA Shigeki
• 金额: $ 12.65万
• 依托单位: Tohoku University (2010-2011)Osaka University (2009)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-21244009/
• 关键词: 確率解析; 場の量子論; ラフパス解析; ループ空間; 準古典極限; 最適輸送写像; 確率測度の幾何学; 処罰問題; ループ群; 確率微分方程式; アレクサンドロ; 超縮小性; アレクサンドロフ空間; 新古典不等式

The study subjects and results are as follows: (1) Laplace approximation and the vanishing of L^2-cohomologies of loop groups from the view point of rough path analysis, (2) Studies on semi-classical properties of Hamiltonian in quantum field theory, Studies from the view point of functional integration, (3)Basic results on the geometry of the space of probability measures (4)Basic study on Sobolev spaces on H-convex set in Wiener spaces and penalization problem and basic results for probability theory

研究课题及成果如下：（1）粗路径分析视角下的拉普拉斯近似与环群L^2上同调的消失，（2）量子场论中哈密顿量的半经典性质研究，从泛函积分的角度进行研究，（3）概率测度空间几何的基本结果（4）维纳空间中H凸集的Sobolev空间和惩罚问题的基础研究以及概率论的基本结果

项目成果

Sets of finite perimeter and the Hausdorff-Gauss measure on the Wiener space

维纳空间上的有限周长集和豪斯多夫-高斯测度

• DOI: 10.1016/j.jfa.2009.06.033
• 发表时间: 2010
• 期刊: J.Funct.Anal
• 作者: Matsuda;Y;Imaruoka;T.;Kunimi;M.;Matsumoto K;& Matsui. M;Masanori Hino
• 通讯作者: Masanori Hino

A WIENER INTEGRAL APPROACH TO NON-COMMUTATIVE HARMONIC OSCILLATORS

非交换谐波振荡器的维纳积分法

• DOI: 10.2206/kyushujm.63.347
• 发表时间: 2009
• 期刊: Kyushu Journal of Mathematics
• 影响因子: 0.4
• 作者: Go Ogiya;Masao Mori;Tomoaki Ishiyama;Andreas Burkert;Setsuo Taniguchi
• 通讯作者: Setsuo Taniguchi

Semi-classical limit of the lowest eigenvalue of a Schrodinger operator on a Wiener space: II.P(φ)_2 -model on a finite volume

维纳空间上薛定谔算子最低特征值的半经典极限：有限体积上的 II.P(φ)_2 模型

• DOI: 10.1016/j.jfa.2008.10.001
• 发表时间: 2009
• 期刊: J.Funct.Anal
• 作者: Shibuya;Ouchi,.. Yuma;et al.;T.Yamamoto;Shigeki Aida
• 通讯作者: Shigeki Aida

Strong uniqueness for both Dirichlet operators and stochastic dynamics to Gibbs measures on a path space with exponential interactions

• DOI: 10.1016/j.jfa.2011.09.023
• 发表时间: 2010-06
• 期刊: Journal of Functional Analysis
• 影响因子: 1.7
• 作者: S. Albeverio;Hiroshi Kawabi;M. Rockner

Limiting behaviors of the Brownian motions on hyperbolic spaces Colloquim Mathematicum

双曲空间上布朗运动的极限行为 Colloquim Mathematicum

• 发表时间: 2010
• 作者: S. Katayama;T. Ozawa;H. Sunagawa;Hiroyuki Matsumoto
• 通讯作者: Hiroyuki Matsumoto