Random fields and the geometry of Wiener space

• Autores: Jonathan E. Taylor, Sreekar Vadlamani
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 4, 2013, págs. 2724-2754
• Idioma: inglés
• DOI: 10.1214/11-AOP730
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• Resumen

  • 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⊂Rk under the standard Gaussian law N(0,Ik×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.