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.

Full Text

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},
  MRNUMBER = {MR2432762},
       URL = {http://mfat.imath.kiev.ua/article/?id=454},
}