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

We deal with Lytvynov's generalization of the chaotic representation property and the corresponding spaces of regular generalized functions in the Levy 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.