Privault, Nicolas Chaotic decompositions on Poisson space and applications. (Décompositions chaotiques sur l’espace de Poisson et applications.) (French) Zbl 0781.60044 C. R. Acad. Sci., Paris, Sér. I 317, No. 4, 385-388 (1993). 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 Keywords:chaotic decomposition on Poisson space; annihilation operator; Wiener- Poisson decomposition PDFBibTeX XMLCite \textit{N. Privault}, C. R. Acad. Sci., Paris, Sér. I 317, No. 4, 385--388 (1993; Zbl 0781.60044)