Poisson process Fock space representation, chaos expansion and covariance inequalities

Reference:

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.

Related documents:

Official URL:

http://dx.doi.org/10.1007/s00440-010-0288-5

Related URLs:

• http://arxiv.org/abs/0909.3205v1

Abstract

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.

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