Polarity of points for Gaussian random fields

Robert C. Dalang ^[1] ; Carl Mueller ^[2] ; Yimin Xiao ^[3]
1. [1] Swiss Federal Institute of Technology in Zurich
  
  Swiss Federal Institute of Technology in Zurich
  
  Zürich, Suiza
2. [2] University of Rochester
  
  University of Rochester
  
  City of Rochester, Estados Unidos
3. [3] Michigan State University
  
  Michigan State University
  
  City of East Lansing, Estados Unidos
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Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 6, 2, 2017, págs. 4700-4751
Idioma: inglés
DOI: 10.1214/17-AOP1176
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Resumen
- We show that for a wide class of Gaussian random fields, points are polar in the critical dimension. Examples of such random fields include solutions of systems of linear stochastic partial differential equations with deterministic coefficients, such as the stochastic heat equation or wave equation with space–time white noise, or colored noise in spatial dimensions k≥1k≥1. Our approach builds on a delicate covering argument developed by M. Talagrand [Ann. Probab. 23 (1995) 767–775; Probab. Theory Related Fields 112 (1998) 545–563] for the study of fractional Brownian motion, and uses a harmonizable representation of the solutions of these stochastic PDEs.