Asymptotic estimates of oscillatory integrals on abstract Wiener space

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型的期望，并计算了其精确形式（与Ikeda和Kusuoka合作）。Kotani对随机媒体进行了广泛的研究。在他的研究中，出现了Feynman-Kac类型的期望作为格林函数的概率表示。我们发现他们之间几乎是一一对应的。这次通信将会有进一步的进展。对于与Wiener空间随机分析相关的另一个研究领域，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得到了关于某些布朗泛函的概率分布的结果。Mitoma和Shigekaw在规范理论和环群领域取得了一些成果。Atsuji得到了Kaehler流形上的全纯映射和全胚扩散的一些结果。其他活动：我们邀请了J.Bertoin和B.Ryabko教授讨论相关话题。我们形成了数学系与巴黎大学概率组的交流项目。

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.