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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".


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Article Information

TitleNotes on Wick calculus on parametrized test functions spaces of Meixner white noise
SourceMethods Funct. Anal. Topology, Vol. 17 (2011), no. 2, 150-167
MathSciNet MR2849475
CopyrightThe 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 


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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},
}


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