Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels
The author gives the Malliavin calculus for Wiener functionals with a parameter and asymptotic expansion formulae for generalized Wiener functionals with a parameter. He also gives short-time asymptotics of heat kernels as an application. This is essentially a modification and an extension of \textit{J. M. Bismut}'s work [Large deviations and the Malliavin calculus (1984; Zbl 0537.35003)]. However, the method of this paper is much simpler and the asymptotic formulae given in this paper are much more practical in computation. Using the method of this paper, one can think in the framework of usual Ito calculus and Malliavin calculus and so it is not necessary to introduce a new heavy framework. This is one of the big advantages. This paper is also a nice review on the Malliavin calculus.
Malliavin calculus for Wiener functionals
scientific article; zbMATH DE number 4030650