Poisson process Fock space representation, chaos expansion and covariance inequalities
Last, G. and Penrose, M. D., 2011. Poisson process Fock space representation, chaos expansion and covariance inequalities. Probability Theory and Related Fields, 150 (3-4), pp. 663-690.
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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-It 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 Poincar, 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.
|Creators||Last, G.and Penrose, M. D.|
|Departments||Faculty of Science > Mathematical Sciences|
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