Poisson stochastic integration in Hilbert spaces
| Nicolas Privault |
|
Jiang-Lun Wu |
| Université de la Rochelle |
|
Institut für Mathematik |
| Avenue Marillac |
|
Ruhr-Universität Bochum |
| 17042 La Rochelle Cedex 1 |
|
D-44780 Bochum |
| France |
|
Germany |
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 multi-parameter time.
Key words: Poisson random measures, Anticipating
stochastic integrals,
Quantum spectral stochastic integrals, Fock space.
Mathematics Subject Classification (1991):
60G60, 60J75, 60H05, 81S25.
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