Generalised Clark-Ocone formulae for differential forms
Probability
2012-06-27 v3
Abstract
We generalise the Clark-Ocone formula for functions to give analogous representations for differential forms on the classical Wiener space. Such formulae provide explicit expressions for closed and co-closed differential forms and, as a by-product, a new proof of the triviality of the L^2 de Rham cohomology groups on the Wiener space, alternative to Shigekawa's approach [16] and the chaos-theoretic version [18]. This new approach has the potential of carrying over to curved path spaces, as indicated by the vanishing result for harmonic one-forms in [6]. For the flat path group, the generalised Clark-Ocone formulae can be proved directly using the It\^o map.
Cite
@article{arxiv.1111.1194,
title = {Generalised Clark-Ocone formulae for differential forms},
author = {Yuxin Yang},
journal= {arXiv preprint arXiv:1111.1194},
year = {2012}
}