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Kachanovsky, N. A.
Clark - Ocone type formulas on spaces of test and generalized functions of Meixner white noise analysis [] !Otitkn.pft: FILE NOT FOUND! !oizd.pft: FILE NOT FOUND! !ospec.pft: FILE NOT FOUND! !oistaspk_H.pft: FILE NOT FOUND! Рубрикатор НБУВ: Тематичні рубрики:
Шифр журнала:
Анотація: In the classical Gaussian analysis the Clark - Ocone formula can be written in the form $E F~, where the function (the random variable) IFD is square integrable with respect to the Gaussian measure and differentiable by Hida; BED denotes the expectation; BED; VtD denotes the conditional expectation with respect to the full $E sigma-algebra that is generated by a Wiener process IWD up to the point of time ItD; $E del .F is the Hida derivative of IFD; $E int~omicron (t)dW sub t denotes the Ito stochastic integral with respect to the Wiener process. This formula has applications in the stochastic analysis and in the financial mathematics. In this paper we generalize the Clark - Ocone formula to spaces of test and generalized functions of the so-called Meixner white noise analysis, in which instead of the Gaussian measure one uses the so-called generalized Meixner measure $E mu (depending on parameters, $E mu can be the Gaussian, Poissonian, Gamma measure etc.). In particular, we study properties of integrands in our (Clark - Ocone type) formulas. !oprip481_H.pft: FILE NOT FOUND!
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