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Chaotic decompositions on Poisson space and applications. (Décompositions chaotiques sur l’espace de Poisson et applications.) (French) Zbl 0781.60044

Summary: Starting from a discrete chaotic decomposition on Poisson space with its annihilation operator, we obtain the operators of derivation and divergence of the continuous-time stochastic calculus of variations. We apply those results to the representation of functionals of the Poisson process in the Wiener-Poisson decomposition.

MSC:

60H05 Stochastic integrals
46N30 Applications of functional analysis in probability theory and statistics
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