The Annals of Probability

Rademacher's Theorem for Wiener Functionals

O. Enchev and D. W. Stroock

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Abstract

Given an $\mathbb{R}$-valued, Borel measurable function $F$ on an abstract Wiener space $(E, H, \mu)$, we show that $F$ is uniformly Lipschitz continuous in the directions of $H$ if and only if it has one derivative in the sense of Malliavin and that derivative is an element of $L^\infty(\mu; H)$.

Article information

Source
Ann. Probab., Volume 21, Number 1 (1993), 25-33.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176989392

Digital Object Identifier
doi:10.1214/aop/1176989392

Mathematical Reviews number (MathSciNet)
MR1207214

Zentralblatt MATH identifier
0773.60042

JSTOR
links.jstor.org

Subjects
Primary: 60H07: Stochastic calculus of variations and the Malliavin calculus
Secondary: 26B05: Continuity and differentiation questions

Keywords
Wiener functionals Malliavin derivative

Citation

Enchev, O.; Stroock, D. W. Rademacher's Theorem for Wiener Functionals. Ann. Probab. 21 (1993), no. 1, 25--33. doi:10.1214/aop/1176989392. https://projecteuclid.org/euclid.aop/1176989392


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