Bismut's gradient formula for vector bundles
Probability
2016-01-12 v1
Abstract
We prove a general Bismut's formula for the gradient of a class of smooth Wiener functionals over vector bundles of a compact Riemannian manifold. This general formula can be used repeatedly for obtaining probabilistic representation of higher order covariant derivatives of solutions of the heat equation similar to the classical Bismut's representation for the covariant gradient of the heat kernel.
Cite
@article{arxiv.1601.02285,
title = {Bismut's gradient formula for vector bundles},
author = {Elton P. Hsu and Zhenan Wang},
journal= {arXiv preprint arXiv:1601.02285},
year = {2016}
}