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

K. D. Elworthy; Yves Le Jan; Xue-Mei Li

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arXiv · 1911.09739

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

K. D. Elworthy·Yves Le Jan·Xue-Mei Li

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Abstract

Integration by parts formulae 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 LeJan-Watanabe connection.

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K. D. Elworthy, Yves Le Jan, Xue-Mei Li. 2019-11-21. Integration by parts formulae for degenerate diffusion measures on path spaces and diffeomorphism groups. https://arxiv.org/abs/1911.09739

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