## The Annals of Probability

### Random fields and the geometry of Wiener space

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 3 July 2013

https://projecteuclid.org/euclid.aop/1372859765

Digital Object Identifier
doi:10.1214/11-AOP730

Mathematical Reviews number (MathSciNet)
MR3112930

Zentralblatt MATH identifier
1284.60100

#### Citation

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. https://projecteuclid.org/euclid.aop/1372859765

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