Bismut type formulae for differential forms

Abstract

Formulae are given for $d{P}_t\varphi$, $d^{\ast }{P}_t\varphi$ and $\Delta P_t\varphi$ for $P_t$ the heat semigroup acting on a q-form $\varphi$. The formulae are Brownian motion expectations of $\varphi$ composed with random translations determined by Weitzenbock curvarure terms. Derivatives of the curvature are not involved.

References in corpus (4)

• Formulae for the derivatives of heat semigroups
• Stochastic Flows on Non-compact Manifolds
• A class of integration by parts formulae in stochastic analysis I
• Integration by parts formulae for degenerate diffusion measures on path spaces and diffeomorphism groups

Cited by in corpus (5)

• An L2 theory for differential forms on path spaces I
• Hessian heat kernel estimates and Calderón-Zygmund inequalities on complete Riemannian manifolds
• Evolution systems of measures and semigroup properties on evolving manifolds
• Some family of q-vector fields on path spaces
• Derivatives of Feynman-Kac Semigroups