Details

Autor(en) / Beteiligte

• Last, Günter
• Penrose, Mathew D.

Titel

Poisson process Fock space representation, chaos expansion and covariance inequalities

Ist Teil von

• Probability theory and related fields, 2011-08, Vol.150 (3-4), p.663-690

Ort / Verlag

Berlin/Heidelberg: Springer-Verlag

Erscheinungsjahr

2011

Link zum Volltext

Quelle

Business Source Ultimate

Beschreibungen/Notizen

• 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–Itô 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 Poincaré 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 .