Open Access
July 2013 Random fields and the geometry of Wiener space
Jonathan E. Taylor, Sreekar Vadlamani
Ann. Probab. 41(4): 2724-2754 (July 2013). DOI: 10.1214/11-AOP730


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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Jonathan E. Taylor. Sreekar Vadlamani. "Random fields and the geometry of Wiener space." Ann. Probab. 41 (4) 2724 - 2754, July 2013.


Published: July 2013
First available in Project Euclid: 3 July 2013

zbMATH: 1284.60100
MathSciNet: MR3112930
Digital Object Identifier: 10.1214/11-AOP730

Primary: 60G60 , 60H05 , 60H07
Secondary: 53C65

Keywords: Malliavin calculus , Random fields , Wiener space

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.41 • No. 4 • July 2013
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