The author has previously constructed a class of admissible vector fields on the path space of an elliptic diffusion process $x$ taking values in a closed compact manifold. In this Note the existence of flows for this class of vector fields is established and it is shown that the law of $x$ is quasi-invariant under these flows.
Analysis on Path Spaces over Riemmannian Manifolds with Boundary
Transportation-Cost Inequalities on Path Space Over Manifolds with Boundary
Horizontal diffusion in $C^1$ path space
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