TY - JOUR
AU - Kachanovsky, N.A.
AU - Kachanovska, T.O.
PY - 2019/06/30
Y2 - 2024/05/20
TI - Interconnection between Wick multiplication and integration on spaces of nonregular generalized functions in the Lévy white noise analysis
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 11
IS - 1
SE - Scientific articles
DO - 10.15330/cmp.11.1.70-88
UR - https://journals.pnu.edu.ua/index.php/cmp/article/view/1510
SP - 70-88
AB - <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>
ER -