TY - JOUR
AU - Kachanovsky, N.A.
PY - 2022/06/23
Y2 - 2024/11/01
TI - On Wick calculus and its relationship with stochastic integration on spaces of regular test functions in the Lévy white noise analysis
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 14
IS - 1
SE - Scientific articles
DO - 10.15330/cmp.14.1.194-212
UR - https://journals.pnu.edu.ua/index.php/cmp/article/view/5535
SP - 194-212
AB - <p>We deal with spaces of regular test functions in the Lévy white noise analysis, which are constructed using Lytvynov's generalization of a chaotic representation property. Our aim is to study properties of Wick multiplication and of Wick versions of holomorphic functions, and to describe a relationship between Wick multiplication and integration, on these spaces. More exactly, we establish that a Wick product of regular test functions is a regular test function; under some conditions a Wick version of a holomorphic function with an argument from the space of regular test functions is a regular test function; 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 with respect to a Lévy process; establish an analog of this result for a Pettis integral (a weak integral); obtain a representation of the extended stochastic integral via formal Pettis integral from the Wick product of the original integrand by a Lévy white noise. As an example of an application of our results, we consider an integral stochastic equation with Wick multiplication.</p>
ER -