@article{Kachanovsky_Kachanovska_2019, title={Interconnection between Wick multiplication and integration on spaces of nonregular generalized functions in the Lévy white noise analysis}, volume={11}, url={https://journals.pnu.edu.ua/index.php/cmp/article/view/1510}, DOI={10.15330/cmp.11.1.70-88}, abstractNote={<p>We deal with spaces of nonregular generalized functions in the Lévy white noise analysis, which are constructed using Lytvynov’s generalization of a chaotic representation property. Our aim is to describe a relationship between Wick multiplication and integration on these spaces. More exactly, we show that when employing the Wick multiplication, it is possible to take a time-independent multiplier out of the sign of an extended stochastic integral; establish an analog of this result for a Pettis integral (a weak integral); and prove a theorem about a representation of the extended stochastic integral via the Pettis integral from the Wick product of the original integrand by a Lévy white noise. As examples of an application of our results, we consider some stochastic equations with Wick type nonlinearities.</p>}, number={1}, journal={Carpathian Mathematical Publications}, author={Kachanovsky, N.A. and Kachanovska, T.O.}, year={2019}, month={Jun.}, pages={70–88} }