Multiple stochastic integral expansions of arbitrary Poisson jump times functionals

We compute the Wiener-Poisson expansion of square-integrable functionals of a finite number of Poisson jump times in series of multiple Poisson stochastic integrals. Key words: Fock space, Poisson process, Wiener chaos. Mathematics Subject Classification (1991): 60J75, 60H05. 1 Introduction Any square-integrable functional on the Wiener, resp. Poisson space can be expanded into a series of multiple stochastic integrals with respect to the Wiener, resp. Poisson process. This property is known as the Wiener chaos representation property. On the Wiener space, the chaos expansion of a functional of d independent single stochastic integrals can be computed using Wiener-Hermite orthogonal expansions. More generally, the gradient operator on Fock space allows to compute the expansion of certain square-integrable functionals, cf. [8]. However, on the Poisson space this gradient is identified to a finite difference operator whose repeated application leads to complicated expressions. In [7] a..