Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels
type: Item
instance of: scholarly article
title: Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels
zbMATH Open document ID: 0633.60077
author: Shinzo Watanabe
published in: The Annals of Probability
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 28C20
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 58J65
zbMATH DE Number: 4030650
zbMATH Keywords: Sobolev spaces of Wiener functionals
zbMATH Keywords: asymptotics of heat kernels
zbMATH Keywords: Malliavin calculus for Wiener functionals
zbMATH Keywords: generalized Wiener functionals
reviewed by: Shigeo Kusuoka
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992255
OpenAlex ID: W1985377459
DOI: 10.1214/AOP/1176992255
description: scientific article; zbMATH DE number 4030650