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AN EXTENDED STOCHASTIC INTEGRAL AND A WICK CALCULUS ON PARAMETRIZED KONDRATIEV-TYPE SPACES OF MEIXNER WHITE NOISE

N. A. KACHANOVSKY

Institute of Mathematics, National Academy of Sciences of Ukraine, 3, Tereschenkivska street, Kyiv, 01601, Ukraine

https://doi.org/10.1142/S0219025708003270Cited by:3 (Source: Crossref)

Abstract

Using a general approach that covers the cases of Gaussian, Poissonian, Gamma, Pascal and Meixner measures, we consider an extended stochastic integral and construct elements of a Wick calculus on parametrized Kondratiev-type spaces of generalized functions; consider the interconnection between the extended stochastic integration and the Wick calculus; and give an example of a stochastic equation with a Wick-type nonlinearity. The main results consist of studying the properties of the extended (Skorohod) stichastic integral subject to the particular spaces under consideration; and of studying the properties of a Wick product and Wick versions of holomorphic functions on the parametrized Kondratiev-type spaces. These results are necessary, in particular, in order to describe properties of solutions of normally ordered white noise equations in the "Meixner analysis".

Keywords:

AMSC: 60H05, 46F05, 60H20

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