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# A stochastic integral of operator-valued functions

### Abstract

In this note we define and study a Hilbert space-valued stochastic integral of operator-valued functions with respect to Hilbert space-valued measures. We show that this integral generalizes the classical Ito stochastic integral of adapted processes with respect to normal martingales and the Ito integral in a Fock space.

Key words: Stochastic integral, resolution of identity, normal martingale, Fock space.

### Article Information

 Title A stochastic integral of operator-valued functions Source Methods Funct. Anal. Topology, Vol. 14 (2008), no. 2, 132-141 MathSciNet MR2432762 Milestones Received 16/01/2008 Copyright The Author(s) 2008 (CC BY-SA)

### Authors Information

Volodymyr Tesko
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

### Citation Example

Volodymyr Tesko, A stochastic integral of operator-valued functions, Methods Funct. Anal. Topology 14 (2008), no. 2, 132-141.

### BibTex

@article {MFAT454,
AUTHOR = {Tesko, Volodymyr},
TITLE = {A stochastic integral of operator-valued functions},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {14},
YEAR = {2008},
NUMBER = {2},
PAGES = {132-141},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=454},
}