Integration by parts and quasi-invariance for the horizontal Wiener measure on a foliated compact manifold

TL;DR

This paper establishes integration by parts formulas and quasi-invariance properties for the horizontal Wiener measure on foliated manifolds, advancing the understanding of stochastic analysis in geometric contexts.

Contribution

It introduces new integration by parts formulas and demonstrates quasi-invariance of the horizontal Wiener measure on foliated manifolds, extending stochastic analysis tools to geometric settings.

Findings

Proved several versions of Driver's integration by parts formula.

Established quasi-invariance of the horizontal Wiener measure.

Applied results to totally geodesic Riemannian foliations.

Abstract

We prove several versions of Driver's integration by parts formula for the horizontal Wiener measure on a totally geodesic Riemannian foliation and prove that the horizontal Wiener measure has a quasi-invariance property with respect to flows generated by suitable tangent processes.