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November 2017 Polarity of points for Gaussian random fields
Robert C. Dalang, Carl Mueller, Yimin Xiao
Ann. Probab. 45(6B): 4700-4751 (November 2017). DOI: 10.1214/17-AOP1176

Abstract

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.

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Robert C. Dalang. Carl Mueller. Yimin Xiao. "Polarity of points for Gaussian random fields." Ann. Probab. 45 (6B) 4700 - 4751, November 2017. https://doi.org/10.1214/17-AOP1176

Information

Received: 1 May 2015; Revised: 1 November 2016; Published: November 2017
First available in Project Euclid: 12 December 2017

zbMATH: 06838131
MathSciNet: MR3737922
Digital Object Identifier: 10.1214/17-AOP1176

Subjects:
Primary: 60G15, 60G60, 60J45

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 6B • November 2017
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