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.

Full Text

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},
}