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The theory and application of Malliavin calculus. (Japanese) Zbl 0698.60045
This is the second part of the author’s advanced exposition of the Malliavin calculus [for the first part see ibid. 36, 97-109 (1984; Zbl 0585.60066)]. These two excellent expositions give us a brief idea of the Malliavin calculus and its applications. The Malliavin calculus is considered as an infinite-dimensional version of the Sobolev theory of generalized functions. After a brief introduction on stochastic differential equations on manifolds, the following three topics, which have been developed in the recent 5 years, are reviewed:
1) Large deviations related to the probabilistic proof of the index theorem. 2) Asymptotic expansions of the fundamental solutions of degenerate heat equations. 3) Degree theory for Wiener maps.
Reviewer: S.Takenaka

60H07 Stochastic calculus of variations and the Malliavin calculus