Asymptotic estimates of oscillatory integrals on abstract Wiener space

抽象维纳空间上振荡积分的渐近估计

• 批准号: 10440043
• 负责人: MANABE Shojiro
• 金额: $ 7.81万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B).
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-10440043/
• 关键词: Wiener space; stochastic analysis; stochastic oscillatory integral; ウィナー空間

On the subject of stochastic oscillatory integrals, Manabe has studied the expectation of Feynman-Kac type having quadratic Brownian functional as its phase function and calculated its exact form (joint work with Ikeda and Kusuoka). Kotani has studied random media extensively. In his study, there appears the expectation of Feynman-Kac type as probabilistic representation of Green function. we found almost one-to-one correspondence between them. This correspondence will promise further progress.Concerning another fields of interests related with stochastic analysis of Wiener space, we mention precise study of Brownian motion, relation with gauge theory and value distribution theory of holomorphic mapping, following results are obtained : Kotani-Isozaki have a result concerning probability distribution of some Brownian functional. Mitoma and Shigekaw obtained some results in the fields of gauge theory and loop group. Atsuji obtained some results concerning holomorphic mapping and holomourphic diffusion on Kaehler manifold.Other activities : We invited professors J.Bertoin and B.Ryabko for discussing related topics. We have formed exchange program between our Math.department and the probability group of University of Pais 6.

在随机振荡积分方面，Manabe 研究了以二次布朗泛函为相函数的 Feynman-Kac 型期望，并计算了其精确形式（与 Ikeda 和 Kusuoka 共同工作）。小谷对随机媒体进行了广泛的研究。在他的研究中，出现了 Feynman-Kac 类型作为格林函数的概率表示的期望。我们发现他们之间几乎是一一对应的。这一通信将有望取得进一步的进展。关于与维纳空间随机分析相关的另一个兴趣领域，我们提到了布朗运动的精确研究、与规范理论的关系以及全纯映射的值分布理论，得到了以下结果： Kotani-Isozaki 得到了有关某些布朗泛函概率分布的结果。 Mitoma和Shigekaw在规范理论和环群领域取得了一些成果。 Atsuji在Kaehler流形上的全纯映射和全纯扩散方面取得了一些成果。其他活动：我们邀请了J.Bertoin和B.Ryabko教授来讨论相关话题。我们的数学系与佩斯第六大学概率组之间建立了交换项目。

项目成果

Y.Isozaki and S.Kotani: "Asymptotic estimates for the first hitting time of fluctuating additive functionals of Brownian motion"Seminaire de Probabilites 34 (Lecture Notes in Mathematics). 374-387 (2000)

Y.Isozaki 和 S.Kotani：“布朗运动波动加性泛函第一次击中时间的渐近估计”Seminaire de Probabilites 34（数学讲义）。

Y.Isozaki and S.Kotani: "Asymptotic estimates for the first hitting time of fluctuating additive functionals of Brownian motion"Seminaire de Protabilite's 34 (Lecture Notes in Mathematics). 374-387 (2000)

Y.Isozaki 和 S.Kotani：“布朗运动波动加性泛函的第一次命中时间的渐近估计”Seminaire de Protabilites 34（数学讲义）。

A.Atsuji: "A Casorati-Weierstrass theorem for holomorphic maps and invariants-fields of holomorphic diffusions"Bull.Sci.math.. 123. 371-383 (1999)

A.Atsuji：“全纯映射和全纯扩散不变量场的 Casorati-Weierstrass 定理”Bull.Sci.math.. 123. 371-383 (1999)

A.Atsuji: "Remarks on harmonic maps into a cone from stochastically complete manifolds"Proc.Japan.Acad.. 75. 105-108 (1999)

A.Atsuji：“关于从随机完备流形到圆锥的调和映射的评论”Proc.Japan.Acad.. 75. 105-108 (1999)

Y.Isozaki: "A cluster of sets of exceptional times of linear Brownian motion"Osaka J.Math.. (2001)

Y.Isozaki：“线性布朗运动的异常时间的一组簇”Osaka J.Math..（2001）