An L2 theory for differential forms on path spaces I
概率论
2016-05-09 v1
摘要
An L2 theory of differential forms is proposed for the Banach manifold of continuous paths on Riemannian manifolds M furnished with its Brownian motion measure. Differentiation must be restricted to certain Hilbert space directions, the H-tangent vectors. To obtain a closed exterior differential operator the relevant spaces of differential forms, the H-forms, are perturbed by the curvature of M. A Hodge decomposition is given for L2 H-one-forms, and the structure of H-two -forms is described. The dual operator d* is analysed in terms of a natural connection on the H-tangent spaces. Malliavin calculus is a basic tool.
引用
@article{arxiv.math/0612416,
title = {An L2 theory for differential forms on path spaces I},
author = {K. D. Elworthy and Xue-Mei Li},
journal= {arXiv preprint arXiv:math/0612416},
year = {2016}
}