Abstract
This paper surveys and compares some recent approaches to stochastic infinite-dimensional geometry on the space $\Gamma$ of configurations (i. e. locally finite subsets) of a Riemannian manifold $M$ under Poisson measures. In particular, different approaches to Bochner–Weitzenböck formulas are considered. A unitary transform is also introduced by mapping functions of $n$ configuration points to their multiple stochastic integral.
Information
Published: 1 January 2002
First available in Project Euclid: 12 June 2015
zbMATH: 1003.60092
MathSciNet: MR1884862
Digital Object Identifier: 10.7546/giq-3-2002-382-394
Rights: Copyright © 2002 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences