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On the relationship between Wick calculus and stochastic integration in the Lévy white noise analysis

  • Maria M. Frei
  • Nikolai A. KachanovskyEmail author
Research Article
  • 1 Downloads

Abstract

We deal with Lytvynov’s generalization of the chaotic representation property and the corresponding spaces of regular generalized functions in the Lévy white noise analysis. Our goal is to find a relationship between the Wick calculus and stochastic integration on these spaces. In particular, we consider the Wick multiplication (a natural multiplication on spaces of generalized functions) under the sign of the stochastic integral, and construct a formal representation of the extended stochastic integral via the Pettis integral, using the Wick product. As application of our results, we consider some stochastic equations with Wick type nonlinearities.

Keywords

Lévy process Extended stochastic integral Wick product 

Mathematics Subject Classification

46F25 60G51 60H05 

Notes

Acknowledgements

The authors are very grateful to the referee for helpful advices.

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Copyright information

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Authors and Affiliations

  1. 1.Precarpathian National UniversityIvano-Frankivs’kUkraine
  2. 2.Institute of MathematicsNASUKievUkraine

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