RANDOM FIELDS AND THE GEOMETRY OF WIENER SPACE

• 成果类型: Article
• 署名作者: Taylor, Jonathan E.; Vadlamani, Sreekar
• 署名单位: Stanford University; Tata Institute of Fundamental Research (TIFR); TIFR Centre for Applicable Mathematics (CAM), Bengaluru
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP730
• 发表日期: 2013
• 页码: 2724-2754
• 关键词: sobolev spaces; excursion sets

摘要

In this work we consider infinite dimensional extensions of some finite dimensional Gaussian geometric functionals called the Gaussian Minkowsld functionals. These functionals appear as coefficients in the probability content of a tube around a convex set D subset of R-k under the standard Gaussian law N(0, I-kxk). 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.