Special Itô maps and an $L^2$ Hodge theory for one forms on path spaces

Abstract

We prove a Kodaira-Hodge decomposition on differential 1-forms on the space of non-smooth paths over a Riemannian manifold, allowing us to define the corresponding first cohomology group. This uses the Itô map of a Brownian system and damped stochastic parallel translation.

References in corpus (2)

• A class of integration by parts formulae in stochastic analysis I
• Concerning the geometry of stochastic differential equations and stochastic flows

Cited by in corpus (1)

• Stochastic Equivariant Cohomologies and Cyclic Cohomology