Abstract
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.
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© 2006 Springer-Verlag Berlin/Heidelberg
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Nualart, D. (2006). Analysis on the Wiener space. In: The Malliavin Calculus and Related Topics. Probability, its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28329-3_1
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DOI: https://doi.org/10.1007/3-540-28329-3_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28328-7
Online ISBN: 978-3-540-28329-4
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