Stochastic integration for abstract, two parameter stochastic processes I. Stochastic processes with finite semivariation in banach spaces

  • Nicolae Dinculeanu


In this paper we define the stochastic integral for two parameter processes with values in a Banach spaceE. We use a measure theoretic approach. To each two parameter processX withX st L E p we associate a measureI X with values inL E p .

IfX isp-summable, i.e. ifI X can be extended to aσ-additive measure with finite semivariation on theσ-algebra of predictable sets, then the integralε HdI X can be defined and the stochastic integral is defined by (H·X) z =ε [0,z] HdI X .

We prove that the processes with finite variation and the processes with finite semivariation are summable and their stochastic integral can be computed pathwise, as a Stieltjes Integral of a special type.


Banach Space Additive Measure Integrable Variation Partial Function Stochastic Integration 


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Copyright information

© Springer 2000

Authors and Affiliations

  • Nicolae Dinculeanu
    • 1
  1. 1.Dept. of MathematicsUniversity of FloridaGainesvilleU.S.A.

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