Poisson process Fock space representation, chaos expansion and covariance inequalities

Poisson process Fock space representation , chaos expansion and covariance inequalities

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 inequal...

On chaos representation and orthogonal polynomials for the doubly stochastic Poisson process

In an L2-framework, we study various aspects of stochastic calculus with respect to the centered doubly stochastic Poisson process. We introduce an orthogonal basis via multilinear forms of the value of the random measure and we analyze the chaos representation property. We revise the structure of non-anticipating integration for martingale random fields and in this framework we study non-antic...

Geometric Methods in Representation Theory Fock Space Representations Fock Space Representations of U Q ( Sl N )

Articles-Karin BAUR: Cluster categories, m-cluster categories and diagonals in polygons-Ada BORALEVI: On simplicity and stability of tangent bundles of rational homogeneous varieties-Laurent EVAIN: Intersection theory on punctual Hilbert schemes-Daniel JUTEAU, Carl MAUTNER and Geordie WILLIAMSON: Perverse sheaves and modular representation theory-Manfred LEHN and Christoph SORGER: A symplectic ...

A Fock space representation for the quantum Lorentz gas

Interacting Fock Space versus Full Fock Module*

We present several examples where moments of creators and annihilators on an interacting Fock space may be realized as moments of creators and annihilators on a full Fock module. Motivated by this experience we answer the question, whether such a possibility exists for arbitrary interacting Fock spaces, in the affirmative sense. We treat the problem in full algebraic generality. As a by-product...