Bismut's gradient formula for vector bundles
  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. 
Elton P. Hsu and Zhenan Wang
math.PR