Special It\^o maps and an $L^2$ Hodge theory for one forms on path spaces
Probability
2019-11-22 v1
Abstract
We prove a Kodaira-Hodge decomposition on differential 1-forms on the space of non-smooth paths over a Riemannian manifold, allowing us to define the corresponding first cohomology group. This uses the It\^o map of a Brownian system and damped stochastic parallel translation.
Keywords
Cite
@article{arxiv.1911.09618,
title = {Special It\^o maps and an $L^2$ Hodge theory for one forms on path spaces},
author = {K. D. Elworthy and Xue-Mei Li},
journal= {arXiv preprint arXiv:1911.09618},
year = {2019}
}