Integration by parts formulae for degenerate diffusion measures on path spaces and diffeomorphism groups
Probability
2019-11-25 v1
Abstract
Integration by parts formulae are given for a class of measures on the space of paths of a smooth manifold determined by the laws of degenerate diffusions. The mother of such formulae, on the path space of diffeomorphism group of 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.
Cite
@article{arxiv.1911.09739,
title = {Integration by parts formulae for degenerate diffusion measures on path spaces and diffeomorphism groups},
author = {K. D. Elworthy and Yves Le Jan and Xue-Mei Li},
journal= {arXiv preprint arXiv:1911.09739},
year = {2019}
}