Geometric aspects of Malliavin's calculus on vector bundles
type: Item
instance of: scholarly article
title: Geometric aspects of Malliavin's calculus on vector bundles
zbMATH Open document ID: 0619.60064
author: Hiroshi Akiyama
published in: Journal of Mathematics of Kyoto University
publication date: 1986-01-01T00:00:00Z
review text: This paper gives differential geometric aspects to Malliavin's stochastic calculus of variations. Let E be a \(C^{\infty}\) real vector bundle over a \(C^{\infty}\) manifold M. Integration by parts formulas are then derived for the composite of M-valued ''smooth and non-degenerate'' Wiener functionals and covariant derivatives of \(C^{\infty}\) cross sections of E in the case where a linear connection is given in E. Moreover, the composite of M-valued ''smooth and non-degenerate'' Wiener functionals and section distributions of E is set up. When E is a Riemannian vector bundle and M is compact and Riemannian, this result is applied to probabilistic expressions of heat kernels of heat equations for E-valued differential forms.
Mathematics Subject Classification ID: 60H99
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 53C99
Mathematics Subject Classification ID: 58J65
zbMATH DE Number: 4005276
zbMATH Keywords: section distributions
zbMATH Keywords: heat kernels
zbMATH Keywords: Malliavin's stochastic calculus of variations
zbMATH Keywords: vector bundle
zbMATH Keywords: Wiener functionals
zbMATH Keywords: Riemannian vector bundle
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250520835
OpenAlex ID: W1545544080
DOI: 10.1215/KJM/1250520835
description: scientific article; zbMATH DE number 4005276