Poisson stochastic integration in Hilbert spaces

Abstract This paper aims to construct adaptedness and stochastic integration on Poisson space in the abstract setting of Hilbert spaces with minimal hypothesis, in particular without use of any notion of time or ordering on index sets. In this framework, several types of stochastic integrals are considered on simple processes and extended to larger domains. The results obtained generalize the existing constructions in the Wiener case, unify them, and apply to multiparameter time.