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Rademacher’s theorem for Wiener functionals. (English) Zbl 0773.60042

One considers a functional defined on an abstract Wiener space; the equivalence between a Lipschitz continuity property in the directions of the Hilbert space and the existence of a bounded Malliavin derivative is proved. The proof is followed by a discussion about further problems and an application to a uniqueness result in random maximization problems.

MSC:

60H07 Stochastic calculus of variations and the Malliavin calculus
26B05 Continuity and differentiation questions
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