Analysis on the Wiener space
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.
KeywordsBrownian Motion Derivative Operator Stochastic Integral Wiener Space Complete Orthonormal System
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