Potential Analysis

, 29:65 | Cite as

Stochastic Integration of Operator-Valued Functions with Respect to Banach Space-Valued Brownian Motion

  • J. M. A. M. van Neerven
  • L. Weis
Open Access


Let E be a real Banach space with property (α) and let W Γ be an E-valued Brownian motion with distribution Γ. We show that a function \(\Psi:[0,T]\to{\mathcal L}(E)\) is stochastically integrable with respect to W Γ if and only if Γ-almost all orbits Ψx are stochastically integrable with respect to a real Brownian motion. This result is derived from an abstract result on existence of Γ-measurable linear extensions of γ-radonifying operators with values in spaces of γ-radonifying operators. As an application we obtain a necessary and sufficient condition for solvability of stochastic evolution equations driven by an E-valued Brownian motion.


Stochastic integration in Banach spaces γ-Radonifying operators Property(αMeasurable linear extensions Stochastic evolution equations 

Mathematics Subject Classifications (2000)

Primary 60H05 Secondary 35R15 47B10 60H15 


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Copyright information

© The Author(s) 2008

Authors and Affiliations

  1. 1.Department of Applied Mathematical AnalysisDelft University of TechnologyGA DelftThe Netherlands
  2. 2.Mathematisches Institut ITechnische Universität KarlsruheKarlsruheGermany

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