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".

Full Text

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},
  MRNUMBER = {MR2849475},
       URL = {http://mfat.imath.kiev.ua/article/?id=567},
}