Quasi-Invariance of the Wiener Measure on the Path Space over a Compact Riemannian Manifold

We study a quasi-invariance property of the Wiener measure on the path space over a compact Riemannian manifold which generalizes the well-known Cameron-Martin theorem for euclidean space. This property is used to prove an integration by parts formula for the gradient operator. We use the integration by parts formula to compute explicitly the Ornstein-Uhlenbeck operator in the path space.