Quasi-invariance of the Wiener measure on the path space over a complete Riemannian manifold

We prove a generalization of the Cameron–Martin theorem for a geometrically and stochastically complete Riemannian manifold; namely, the Wiener measure on the path space over such a manifold is quasiinvariant under the flow generated by a Cameron–Martin vector field. © 2009 Elsevier Inc. All rights reserved.