Geometric aspects of Malliavin's calculus on vector bundles
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.
Malliavin's stochastic calculus of variations
scientific article; zbMATH DE number 4005276