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Anticipative calculus for the Poisson process based on the Fock space. (English) Zbl 0701.60048
Séminaire de probabilités XXIV 1988/89, Lect. Notes Math. 1426, 154-165 (1990).
[For the entire collection see Zbl 0695.00024.]
The aim of the paper is to present some properties of the derivative operator D and his adjoint \(\delta\) on a general Fock space, and to analyze their behaviour when the Fock space is interpreted as a Poisson space. The main results are the interpretation of the derivative operator as a translation and the representation of the operator \(\delta\) as a Stieltjes integral on predictable processes. We also introduce a general conditional expectation on the Fock space, and in this case it is possible to obtain a generalized Clark’s formula.
Reviewer: J.Vives

60H05 Stochastic integrals
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