Analysis on the Wiener space

  • David Nualart
Part of the Probability and its Applications book series (PIA)


In this chapter we study the differential calculus on a Gaussian space. That is, we introduce the derivative operator and the associated Sobolev spaces of weakly differentiable random variables. Then we prove the equivalence of norms established by Meyer and discuss the relationship between the basic differential operators: the derivative operator, its adjoint (which is usually called the Skorohod integral), and the Ornstein-Uhlenbeck operator.


Brownian Motion Derivative Operator Stochastic Integral Wiener Space Complete Orthonormal System 


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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • David Nualart
    • 1
  1. 1.Facultat de MatemàtiquesUniversitat de BarcelonaBarcelonaSpain

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