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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.

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},
URL = {http://mfat.imath.kiev.ua/article/?id=419},
}