%0 Journal Article
%T Poisson process Fock space representation, chaos expansion and covariance inequalities
%A Guenter Last
%A Mathew D. Penrose
%J Mathematics
%D 2009
%I arXiv
%X We consider a Poisson process $\eta$ on an arbitrary measurable space with an arbitrary sigma-finite intensity measure. We establish an explicit Fock space representation of square integrable functions of $\eta$. As a consequence we identify explicitly, in terms of iterated difference operators, the integrands in the Wiener-Ito chaos expansion. We apply these results to extend well-known variance inequalities for homogeneous Poisson processes on the line to the general Poisson case. The Poincare inequality is a special case. Further applications are covariance identities for Poisson processes on (strictly) ordered spaces and Harris-FKG-inequalities for monotone functions of $\eta$.
%U http://arxiv.org/abs/0909.3205v1