Polar sets for anisotropic Gaussian random fields

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7 Citations (Scopus)

Abstract

This paper studies polar sets for anisotropic Gaussian random fields, i.e. sets which a Gaussian random field does not hit almost surely. The main assumptions are that the eigenvalues of the covariance matrix are bounded from below and that the canonical metric associated with the Gaussian random field is dominated by an anisotropic metric. We deduce an upper bound for the hitting probabilities and conclude that sets with small Hausdorff dimension are polar. Moreover, the results allow for a translation of the Gaussian random field by a random field, that is independent of the Gaussian random field and whose sample functions are of bounded Hölder norm.

Original languageEnglish
Pages (from-to)840-847
Number of pages8
JournalStatistics & Probability Letters
Volume80
Issue number9-10
DOIs
Publication statusPublished - 2010
Externally publishedYes

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