Multilateral research on infinite dimensional differential operators via stochastic analysis

基于随机分析的无限维微分算子多边研究

• 批准号: 23740107
• 负责人: KAWABI HIROSHI
• 金额: $ 2.75万
• 依托单位: Okayama University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23740107/
• 关键词: 確率解析; 経路空間; 微分作用素; 一意性定理; 確率偏微分方程式; Rough Path理論; 推移確率; 漸近挙動; Gibbs測度; ラフパス解析

I mainly studied uniqueness problems of differential operators and corresponding stochastic dynamics on infinite dimensional spaces via stochastic analysis. In particular, I proved strong uniqueness of Dirichlet operators for Gibbs measures which appear in quantum field theory and constructed a unique solution to the corresponding stochastic PDE by using Dirichlet form theory. Besides, I studied precise asymptotic behavior (i.e., the method of stationary phase) of some oscillatory functional integrals by combining Rough Path theory with Malliavin calculus. Motivated by this study of the stationary phase method, I also obtained an explicit effect of non-symmetry on the long time asymptotic behavior for a class of non-symmetric random walks on the triangular lattice.

我主要研究了微分算子的唯一性问题和相应的随机动力学在无限维空间中的随机分析。特别地，证明了量子场论中出现的Gibbs测度的Dirichlet算子的强唯一性，并利用Dirichlet形式理论构造了相应随机偏微分方程的唯一解.此外，我研究了精确的渐近行为（即，稳定相法），并将粗糙路径理论与Malliavin积分相结合，给出了一类振荡泛函积分的稳定相法。受定相方法研究的启发，我还得到了三角格点上一类非对称随机游动的非对称性对长时间渐近行为的显式影响。

项目成果

Strong uniqueness of diffusions on a path space with interactions

具有相互作用的路径空间上的扩散具有很强的唯一性

• 发表时间: 2012
• 作者: I. Sim;S. Tanaka;河備 浩司
• 通讯作者: 河備 浩司

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

Uniqueness of Dirichlet forms related to stochastic quantization under exponential interaction in two-dimensional finite volume

二维有限体积指数相互作用下随机量子化狄利克雷形式的唯一性

• 发表时间: 2014
• 作者: Hiroshi Kawabi

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

Rockner，“狄利克雷算子和随机动力学在具有指数相互作用的路径空间上的吉布斯测量具有很强的唯一性”

• 发表时间: 2012
• 期刊: J. Funct. Anal
• 作者: S. Albeverio;H. Kawabi and M
• 通讯作者: H. Kawabi and M

Precise asymptotics of functional integrals for infinite dimensional Ito-Lyons map of Brownian rough paths

布朗粗糙路径无限维 Ito-Lyons 图的函数积分的精确渐近

• 发表时间: 2011
• 作者: Hirata;Y.;Terashima;Y.;Anabuki;N.;Nakagawa;T.;Awaki;H.;Masahide Iwakiri;Kengo Tomida;Hiroshi Kawabi
• 通讯作者: Hiroshi Kawabi