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

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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.


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Article Information

TitleOn an extended stochastic integral and the Wick calculus on the connected with the generalized Meixner measure Kondratiev-type spaces
SourceMethods Funct. Anal. Topology, Vol. 13 (2007), no. 4, 338-379
MathSciNet MR2374836
CopyrightThe 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},
       URL = {http://mfat.imath.kiev.ua/article/?id=371},
}


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