Asymptotic estimates of oscillatory integrals on abstract Wiener space

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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.