De Rham–Hodge decomposition and vanishing of harmonic forms by derivation operators on the Poisson space
Date of Issue2016
School of Physical and Mathematical Sciences
We construct differential forms of all orders and a covariant derivative together with its adjoint on the probability space of a standard Poisson process, using derivation operators. In this framewok we derive a de Rham–Hodge–Kodaira decomposition as well as Weitzenböck and Clark–Ocone formulas for random differential forms. As in the Wiener space setting, this construction provides two distinct approaches to the vanishing of harmonic differential forms.
De Rham–Hodge–Kodaira decomposition
Infinite Dimensional Analysis, Quantum Probability and Related Topics
© 2016 World Scientific Publishing Company. This is the author created version of a work that has been peer reviewed and accepted for publication by Infinite Dimensional Analysis, Quantum Probability and Related Topics, World Scientific Publishing Company. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1142/S0219025716500107].