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Integration by parts formulae for degenerate diffusion measures on path spaces and diffeomorphism groups



Integration by parts are given for a class of measures on the space of paths of a smooth manifold M determined by the laws of degenerate diffusions. The mother of such formulae, on the path space of diffeomorphism group of M is shown to arise from a quasi-invariance property of measures determined by stochastic flows. From this the other formulae are derived by filtering out redundant noise using an associated Le Jan-Watanabe connection

Topics: QA
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