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# On an extended stochastic integral and the Wick calculus on the connected with the generalized Meixner measure Kondratiev-type spaces

### Abstract

We introduce an extended stochastic integral and construct elements of the Wick calculus on the Kondratiev-type spaces of regular and nonregular gene alized functions, study the interconnection between the extended stochastic integration and the Wick calculus, and consider examples of stochastic equations with Wick-type nonlinearity. Our researches are based on the general approach that covers the Gaussian, Poissonian, Gamma, Pascal and Meixner analyses.

### Article Information

 Title On an extended stochastic integral and the Wick calculus on the connected with the generalized Meixner measure Kondratiev-type spaces Source Methods Funct. Anal. Topology, Vol. 13 (2007), no. 4, 338-379 MathSciNet MR2374836 Copyright The Author(s) 2007 (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, On an extended stochastic integral and the Wick calculus on the connected with the generalized Meixner measure Kondratiev-type spaces, Methods Funct. Anal. Topology 13 (2007), no. 4, 338-379.

### BibTex

@article {MFAT371,
AUTHOR = {Kachanovsky, N. A.},
TITLE = {On an extended stochastic integral and the Wick calculus on the connected with the generalized Meixner measure Kondratiev-type spaces},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {13},
YEAR = {2007},
NUMBER = {4},
PAGES = {338-379},
ISSN = {1029-3531},
MRNUMBER = {MR2374836},
URL = {http://mfat.imath.kiev.ua/article/?id=371},
}