The Annals of Probability
- Ann. Probab.
- Volume 45, Number 6B (2017), 4700-4751.
Polarity of points for Gaussian random fields
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 $k\geq1$. 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.
Ann. Probab., Volume 45, Number 6B (2017), 4700-4751.
Received: May 2015
Revised: November 2016
First available in Project Euclid: 12 December 2017
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Dalang, Robert C.; Mueller, Carl; Xiao, Yimin. Polarity of points for Gaussian random fields. Ann. Probab. 45 (2017), no. 6B, 4700--4751. doi:10.1214/17-AOP1176. https://projecteuclid.org/euclid.aop/1513069271