Clark-Ocone type formulas on the spaces of regular basic and generalized functions in the analysis of Levy white noise

• Date: 2023
• Author Affiliations: Микола Качановський — Інтистут математики НАН України, м. Київ
• Keywords: keywords
• Main Authors: Kachanovskyy, Mykola, Качановський, Микола
• Format: Article
• Language: Ukrainian
• Published: Інститут математики НАН України 2023
• Online Access: https://trim.imath.kiev.ua/index.php/trim/article/view/529
• Journal Title: Transactions of Institute of Mathematics of NAS of Ukraine

In the classical Gaussian analysis the Clark-Ocone formula can be written in the form $$ F=\mathbf{E}{F}+\int\mathbf{E}\big(\partial_t F|_{\mathcal F_t}\big)\,dW_t, $$ where a function (a random variable) $F$ is square integrable with respect to the Gaussian measure and differentiable by Hida; $\ma...