2009/09/17 by Guenter Last, Last, Guenter, Mathew D. Penrose +1 · 2 citations
Economics, Econometrics and Finance · Mathematics · #60G55 #60H07 #Complex Variables (math.CV) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.0909.3205
openalex publication_date 2009/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a Poisson process η on an arbitrary measurable space with an arbitrary sigma-finite intensity measure. We establish an explicit Fock space representation of square integrable functions of η. 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 η.