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Di Nunno, Giulia; Meyer-Brandis, Thilo; Øksendal, Bernt; Proske, Frank

Malliavin calculus and anticipative Itô formulae for Lévy processes. (English) Zbl 1080.60068

Infin. Dimens. Anal. Quantum Probab. Relat. Top. 8, No. 2, 235-258 (2005).
The forward integral with respect to a pure jump Lévy process is introduced, and an Itô formula is established for such integrals. Using Malliavin calculus, the authors then relate such forward integrals with Skorokhod integrals, which enables them to obtain further an Itô formula for Skorokhod integrals with respect to a pure jump Lévy process.
Reviewer: Michel Sortais (Berlin)

Cited in 61 Documents

MSC:

60H40 White noise theory
60G51 Processes with independent increments; Lévy processes
60H07 Stochastic calculus of variations and the Malliavin calculus
60G57 Random measures

Keywords:

Poisson random measures; white noise; Skorokhod integrals; forward integrals; stochastic derivatives; Wick product
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References:

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