Generalized stochastic derivatives on a space of regular generalized functions of Meixner white noise

Abstract

We introduce and study generalized stochastic derivatives on a Kondratiev-type space of regular generalized functions of Meixner white noise. Properties of these derivatives are quite analogous to the properties of the stochastic derivatives in the Gaussian analysis. As an example we calculate the generalized stochastic derivative of the solution of some stochastic equation with a Wick-type nonlinearity.

Full Text

Article Information

Title	Generalized stochastic derivatives on a space of regular generalized functions of Meixner white noise
Source	Methods Funct. Anal. Topology, Vol. 14 (2008), no. 1, 32-53
MathSciNet	MR2402151
Copyright	The Author(s) 2008 (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, Generalized stochastic derivatives on a space of regular generalized functions of Meixner white noise, Methods Funct. Anal. Topology 14 (2008), no. 1, 32-53.

BibTex

@article {MFAT419,
    AUTHOR = {Kachanovsky, N. A.},
     TITLE = {Generalized stochastic derivatives on a space of regular generalized functions of Meixner white noise},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {14},
      YEAR = {2008},
    NUMBER = {1},
     PAGES = {32-53},
      ISSN = {1029-3531},
  MRNUMBER = {MR2402151},
       URL = {http://mfat.imath.kiev.ua/article/?id=419},
}