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# Notes on Wick calculus on parametrized test functions spaces of Meixner white noise

### Abstract

Using a general approach that covers the cases of Gaussian, Poissonian, Gamma, Pascal and Meixner measures, we construct elements of a Wick calculus on parametrized Kondratiev-type spaces of test 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 in studying properties of a Wick product and Wick versions of holomorphic functions on the parametrized Kondratiev-type spaces of test functions. These results are necessary, in particular, in order to describe properties of solutions of stochastic equations with Wick type nonlinearities in the "Meixner analysis".

### Article Information

 Title Notes on Wick calculus on parametrized test functions spaces of Meixner white noise Source Methods Funct. Anal. Topology, Vol. 17 (2011), no. 2, 150-167 MathSciNet MR2849475 Copyright The Author(s) 2011 (CC BY-SA)

### Authors Information

N. A. Kachanovsky
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

### Citation Example

N. A. Kachanovsky, Notes on Wick calculus on parametrized test functions spaces of Meixner white noise, Methods Funct. Anal. Topology 17 (2011), no. 2, 150-167.

### BibTex

@article {MFAT567,
AUTHOR = {Kachanovsky, N. A.},
TITLE = {Notes on Wick calculus on parametrized test functions spaces of  Meixner white noise},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {17},
YEAR = {2011},
NUMBER = {2},
PAGES = {150-167},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=567},
}