The Annals of Probability

Random fields and the geometry of Wiener space

Jonathan E. Taylor and Sreekar Vadlamani

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In this work we consider infinite dimensional extensions of some finite dimensional Gaussian geometric functionals called the Gaussian Minkowski functionals. These functionals appear as coefficients in the probability content of a tube around a convex set $D\subset\mathbb{R}^{k}$ under the standard Gaussian law $N(0,I_{k\times k})$. Using these infinite dimensional extensions, we consider geometric properties of some smooth random fields in the spirit of [Random Fields and Geometry (2007) Springer] that can be expressed in terms of reasonably smooth Wiener functionals.

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Ann. Probab. Volume 41, Number 4 (2013), 2724-2754.

First available in Project Euclid: 3 July 2013

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Zentralblatt MATH identifier

Primary: 60G60: Random fields 60H05: Stochastic integrals 60H07: Stochastic calculus of variations and the Malliavin calculus
Secondary: 53C65: Integral geometry [See also 52A22, 60D05]; differential forms, currents, etc. [See mainly 58Axx]

Wiener space Malliavin calculus random fields


Taylor, Jonathan E.; Vadlamani, Sreekar. Random fields and the geometry of Wiener space. Ann. Probab. 41 (2013), no. 4, 2724--2754. doi:10.1214/11-AOP730.

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