Clark-Ocone type formulas in the Meixner white noise analysis
Karpatsʹkì Matematičnì Publìkacìï, 2013 In the classical Gaussian analysis the Clark-Ocone formula allows to reconstruct an integrand if we know the Ito stochastic integral. This formula can be written in the form$$F=\mathbf EF+\int\mathbf E\big\{\partial_t F|_{\mathcal F_t}\big\}dW_t,$$where ...
N. A. Kachanovsky
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Karpatsʹkì Matematičnì Publìkacìï, 2014 The operators of stochastic differentiation, which are closely related with the extended Skorohod stochastic integral and with the Hida stochastic derivative, play an important role in the classical (Gaussian) white noise analysis.
M.M. Dyriv, N.A. Kachanovsky
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Karpatsʹkì Matematičnì Publìkacìï, 2016 The operators of stochastic differentiation, which are closely related with the extended Skorohod stochastic integral and with the Hida stochastic derivative, play an important role in the classical (Gaussian) white noise analysis.
N.A. Kachanovsky
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On extended stochastic integrals with respect to Lévy processes
Karpatsʹkì Matematičnì Publìkacìï, 2013 Let $L$ be a Levy process on $[0,+\infty)$. In particular cases, when $L$ is a Wiener or Poisson process, any square integrable random variable can be decomposed in a series of repeated stochastic integrals from nonrandom functions with respect to $L ...
N.A. Kachanovsky
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