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Zbl 0653.60045
Dermoune, A.; Krée, P.; Wu, L.
Calcul stochastiques non adapté par rapport a la mesure aléatoire de Poisson. (Stochastic calculus not adapted to the Poisson random measure). (French)
[A] Séminaire de probabilités XXII, Strasbourg/France, Lect. Notes Math. 1321, 477-484 (1988).

[For the entire collection see Zbl 0635.00013.] \par In the first part of the paper the authors present the chaos decomposition on the Poisson space. \par The second part of the paper is devoted to applications to stochastic calculus. In particular, the divergence operator extends the stochastic integral with respect to the compensated Poisson process and every distribution in $W\sp{2,s}(X)$ with zero mean can be represented in this way [cf. {\it A. S. !stünel}, C. R. Acad. Sci. Paris, Sér. I 300, 277-279 (1985; Zbl 0575.60056) for similar results in the Wiener case]. Finally, a change of variables formula is given.
[P.Kröger]

MSC 2000:: *60H05 Stochastic integrals
60G55 Point processes
60H07 Stochastic calculus of variations and the Malliavin calculus

Keywords: chaos decomposition on the Poisson space; stochastic integral with respect to the compensated Poisson process

Citations: Zbl 0635.00013; Zbl 0575.60056

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